Well, the issue is two fold:

1. The initial battle(s)

2. The aftermath

The Third Battle of the Castle

The Prydwen's destruction cripples the BoS right there in terms of morale and its ability to engage the Minutemen because that's their Vertibird deck and they just lost their God Leader. It's the equivalent of Hitler being blown up in WW2 along with the entire Luftwaffe. There's still plenty of military power but that's a kind of major blow.

What the Minutemen have to do next is survive the Brotherhood of Steel's counterattack. This is a bunch of paladins and knights attacking in revenge for Elder Maxson's death and the deaths of so many others. We don't know if this is meant to be all of the Brothers left in the Capital Wasteland but if not, then it's probably just the forces leftover at the airport (assuming they didn't all die in the crash of the Prydwen because that thing is going down Hindenburg style right on top of them).

In a realistic contest, it's going to be a horrifically epic fight as the Minutemen have fortified the Castle extremely well (presumably), have access to laser weapons, and in a "story" situation, you'd want all of your Companions there. Plus, as mentioned, artillery strikes me as one of the few things which could actually destroy Power Armor assuming the simple equation: Power Armor=Human Tank.

I can assume that, lore wise, the Sole Survivor would probably be wearing his suit himself. Going with a canonical military vet, he's also the only one of the Companions other than Danse (who wouldn't fight for them) who would be trained in its use anyway.

The Minutemen don't have to destroy the Brotherhood here but survive the Counterattack, which is very "doable" I think given you have a dozen hardened veterans (The Companions), however many Minutemen came out of retirement, all of their trainees, and whatever defenses erected on an automatic level. Assaulting a fortified position has historically been an enormous slog even for a well-prepared assault and this isn't going to be one. The Brotherhood of Steel WORSHIPED Elder Maxson and they're insane with anger, rage, and grief.

The Commonwealth versus the Eastern Brotherhood of Steel

BUT if they survive, then the BoS is broken in the Commonwealth. This doesn't mean the Minutemen could win a war against them, though. The Capital Wasteland has had 15 years to rebuild its forces and its entirely possible they may decide to make a full effort to return and destroy the Minutemen and avenge their leader. However, at the end of the day we have to wonder, "How big is the Eastern BoS after 15 years of rebuilding? How much is left after this attack? How much do they want a war?"

If the BOS want a war then, yes, the Sole Survivor is screwed and so is the Commonwealth.

If the Institute was evacuated and a Railroad allied ending was achieved, it may be a bit different.

The Institute will suddenly have to share its vast scientific knowledge with the Wastelanders and there's a near-infinite supply of tireless robot laborers with a loyalty to the Sole Survivor to help them prepare for the BoS. The Sole Survivor might be forced to go into hiding to avoid BoS vengeance. Even so, it's equally likely Maxson's death will create a power struggle.

But that's a story we're never likely to see.

Have you played NV? No really, the game makes it hilariously clear that the NCR are beyond inept at everything they do, literally EVERYTHING. And yet, they still managed to beat the BoS, why? Because they had numbers, they outnumbered the BoS 15-20 to 1, and won basically only because of that reason.

The same holds true of the BoS in the Commonwealth. They are are only a small fraction of the BoS, those that came on the Prydwen airship, and the Minutemen are a volunteer militia made up of local residents. Locals that outnumber the BoS forces..... like 100 to 1, if not more.

The BoS's training and tech doesn't hold jack to sheer numbers. The NCR was beating the BoS because of that reason, and The Legion was holding their own against the NCR, with heavy suggestion that they would beat the NCR at the dam unles The Courier intervened, for the same reason.

To be fair, NCR's campaign of idiocy in the Mojave was not their SOP.

The first War for Hoover Dam was fought with maximum competency, Desert Rangers, Depowered Armor Heavy Troopers, and Boone's snipers with Anti-Material Rifles which can pierce helicopters in RL and probably do the same to power armor.

The BoS battle was probably fought even better.

It required George W. Bush President Kimball and his puppet screwing it up.

https://www.youtube.com/watch?v=yO7nMwEx1HI

Power Armor is insane. It is utterly insane, and so are Gatling Lasers. The Brotherhood of Steel is most certainly a force to be reckoned with. If it were a real war between the Minutemen and the Brotherhood of Steel, the Minutemen would be wiped out.

The Minutemen won because the Brotherhood of Steel didn't account for them -- they were taken by surprise. That's all.

Even with their main base destroyed, BoS Knights are no joke. It takes only a handful of Super Mutants to taken down even a fully maxed out settlement.. and only a handful of Knights to take down an army of Super Mutants.

once your reach a cetain point, quantity becomes a quality

Yes, power armor is awesome.

And the enemy has artillery.

Yes, it's not as sixy as Power Armor but this is a bunch of footsoldiers attacking people with giant cannons.

Also, there's a bunch of Laser turrets and mines in the Armory anyway.

You can use them if you use the Workbench.

The Brotherhood's weakness, as always, is its limited numbers. They can be beaten by a driven force of volunteers that is willing to recruit and train pretty much anyone. Especially with an HQ as vulnerable as the Prydwen it's not too strange that the Minutemen could destroy them.

So basically it's another NV situation.

The player character is the only reason the Minutemen get anything done.

If pipe rifles can take them out, and they do, then artillery would just sweep them from the sky. Vertibirds are paper airplanes! I think this new Brotherhood is having severe resource issues. They must be cobbling these vertibirds out of low grade scrap or something. Their new breed of pilots leave much to be desired as well. I've seen a vertibird just randomly sping out of control and crash into a large road sign. I'm very underwhelmed by this new BoS. They were once my favorite faction, but they've lost their touch.

Here is how I see this playing out,

1) While being ignored by the BoS, build up our settlements to be prosperous towns well defended with heavy laser and rocket turrets, along with artillery installations.

3) Arm minutemen militia with heavy combat armor and a mix of 50 cal sniper rifles and plasma rifles...all tricked out

4) Amass a collection of power armor for the minutement (up to 10 now !) to create an elite fighting force. All of it will be upgraded well above the scrapheap baselines painted rustheap of normal T-60 armor. Apparently BoS tech is low these days...

5) While the BoS still thinks of me as their helpful friend, I'll hitch a ride on the blimp, then destroy everyone that gets in my way. Their defense is so lax that a single attacker in upgraded X-01 power armor with a gauss rifle would sweep the floor with them. Now I have their base! I'll just set it on a crash course for the airport... two birds, one stone

6) They'll have to regroup and likely launch another attack which will involve swarming at towns. Assuming they survive the raiders pipe rifles (unlikely) they'll be torn apart by laser/rocket turrets and artillery once they reach the towns. BoS vertibird tactics involved circling around a target, firing an inaccurate minigun causing light or no damage until either the vertibird is taken out by pipe rifles or it survives long enough to drop a knight or two off. Faced with actual serious firepower, they'd be unlikely to even get their knights down before crashing. If they do, T-60 power armor isn't a great match for heavy laser and rocket turrets... or guards with cover and plasma/50cal rifles.

PS: I hope a patch fixes how hilariously bad vertibirds and their pilots are. Although it does explain why they'd have to recruit a random competent wastelander and promote them to knight within a couple days. They can't handle mere raiders or super mutants on their own. They need someone that can. I really want the BoS to be the awesome high tech military faction it once was... but the presentation in Fallout 4 paints them as the ineffective remnant of a once great force... a bunch of kids that inherited power armor and vertibirds from their fathers, but never learned to use them.

I'm confused at this idea given the Minutemen are re-founded by the PC.

That's kind of their story point.

You build groups for the minute men by helping the farmers and settlers and setting up radio towers for others to join your cause of protecting the innocent, its one guy who amasses an army to fight with him if you do the quests for him.

Well you better tell most armed forces in the world that they are doing it wrong.

Using machine guns from helicopters are very common, using bombs from helicopters are very rare.

Nice plan. I don't think the BOS is the remnant of a once-proud nation and is probably stronger on the East Coast than it has been in the West Coast for years. The thing is, I think there's a medium ground between "brothers of steel are unkillable badasses, the greatest warriors in history" and "Brothers are chumps."

A major theme in the game is the Brotherhood is usually taking a beating when we see them active. I wrote an essay for my blog ( http://unitedfederationofcharles.blogspot.com/2012/08/the-morality-ambiguity-of-brotherhood.html) about how the Lyons Brotherhood wasn't nearly as competent or good as it appears.

They're actively LOSING the war against the Super Mutants when you encounter them and are bitterly divided. The Super Mutants should be as powerful as the Brothers but they get their ass kicked in this game left and right. Likewise, the powered-armored soldiers of America weren't able to defeat the Chinese government in a land-war despite having power-armor and the Chinese, well, not.

Power Armor isn't an "I win" button but just a very useful tool. I liken it to having tanks--usually, it'll do the job but not if they have weapons which can destroy tanks. The Brotherhood can and does beat most factions but in terms of technological progress, power armor and laser guns are simply not noticeably better than high-powered conventional ordinance. Likewise, I think most brothers are very well trained soldiers but they're not noticeably better trained than the soldiers of our time.

Great for beating the puss out of most Wastelanders but not giving them some invincible "I win" button the same way the high level PCs have.

They aren't helicopters, they are VTOL aircrafts. And real machine guns would shred through wooden planks. The whole damage model is pretty unrealistic, but that is not a problem unless it is carried into the story.

The BoS only uses their Vertibirds so inefficient for game play reasons. People would be disappointed if they peeled off before they explode.

A helictoper is a VTOL dude lol

The BoS has no reason to assume the Minutemen were on their side. The BoS is always skeptical towards outsiders and they just retreated from the capital wastelands. They be would concerned if someone build lots of howitzers that could reach them.

But they aren't just helicopters.

In canon, the Sole Survivor is probably a brother until Danse and the Railroad attacks.

They just don't care about the Minutemen. They likely see them as irrelevant.

They don't see the Railroad organization as irrelevant either.

Uh... I know... the Railroad is actively fighting for what the BoS is against.

They don't seem concerned so far. It's one of the weaknesses of open world games though... it is very difficult to have the game account for all the things a player has done. I wish there was more play between the factions though.

I wish the presentation hit within that middle ground, but so far it's been squarely in the 'chumps' side of things. My first encounter with the BoS was a man in power armor being overwhelmed by ghouls. After that, the BoS has me do things for them because they don't have the resources to do it themselves. After that, the BoS shows up in a big way that fizzles. Then I see vertibirds crashing and exploding everywhere fighting even the most trivial of opponents or no opponent at all! They ask me to do more things they can't do... I know the player is supposed to be the starring role, but you'd think they could at least present the BoS as capable of getting stuff done occasionally! I haven't witnessed the BoS win a fight yet. I have no choice but to view them as weak and incapable... all talk and big suits, but no fight.

The institute on the other hand... they seem to dominate any scene I find them involved in. Their presentation is strong and well done.

The BoS only uses their Vertibirds for gameplay reasons so inefficient, but that shouldn't impact the story. Just like it is probably not canon that you can restore health by eating 15 corncobs during an intense firefight.

The BoS could easily destroy the minutemen by attacking their settlements. The BoS is much more mobile, so they could concentrate their power against single targets while most of the Minutemen are at the Castle or scattered through the commonwealth.

I have a theory the BoS assumes the Minutemen are just a bunch of irrelevant Wastelanders if they don't know the Sole Survivor.

And if they do, they assume the SS is bringing the Minutemen men in as BoS support.

Which is insulting and paternalistic.

Danse and Preston's interactions are HILARIOUS by the way. Bring Preston along to the recruitment missions and he will RIP on the BoS A LOT.

If the Prydwen is destroyed, the BOS becomes the opposite of Mobile and the Minutemen seize the surviving Vertibirds at the Airport.

That actually is an interesting twist.

The BOS survivors suddenly have lost air superiority.