Personally, I think it's questionable which *IS* the real Brotherhood of Steel at this point. The California Chapter of the Brotherhood of Steel seems to have been annihilated by the New California Republic. Unless someone makes a new game that clarifies the point, I think people are wrong to think there's this big amount of reinforcements awaiting them.
It's entirely possible that the Mojave Chapter of the BOV is *IT* west of the Midwest (unlikely but possible). Actually, I find this the much more poetic option that the Hidden Bunker is the last remnant of the Brotherhood of Steel and the Elder's position becomes MUCH more understandable. So does Veronica's position.
Elder Lyons, by contrast, is pretty much the ruler of the Capital Wasteland. Rivet City has formally allied with the Brotherhood of Steel, they control the Purifier, the LW may or may not have annihilated the majority of Super Mutants in the Capital Wasteland for the Brotherhood, the LW does the majority of fighting at Adam's Air Force base and now the Brotherhood has a nifty new base of operations.
Since they're basically doing all of Veronica's suggestions, they're more or less transforming into a Feudal Nation-State with Lyons as King. It's like they have all of the "bring back civilization through military force" of Caesar with none of the bad.
If the LW becomes dictator of Pittsburgh, they also have access to the world's first functioning steel works.
Yup. As much as I like Fallout 3 for its own merits, I wish I could just ignore the ending sequence. It made absolutely no sense. The East Coast Brotherhood crapped themselves when the Enclave first showed up (and rightly so) and talked about their inferiority in weapons and armor (and rightly so) but then in the end it was just "oh hey...yeah we managed to get that top-secret robot thingy working so go use it to completely annihilate that group that we feared so much!" Liberty Prime was a freaking joke (I love his catchphrases though) and the Enclave should have mopped the floor with the East Coast based on what I saw in the game. Sarah Lyons and her "pride" didn't do a dang thing, it was one freaking "script shields at 150%" robot that did everything.
The Enclave was potentially already finished by that time, if you recall. The LW can convince JHE to blow up the base with a fairly easy Speech Check or Science Check. If he DOESN'T, the Enclave is just occupying the Purifier with a small garrison. If he DOES blow up Raven Rock, the Enclave is pretty much decapitated leadership wise with a HUGE chunk of their military presumably taken out in the process as well (not to mention probably the entirety of their civilian force).
The only reason the Brotherhood of Steel did so well against the Enclave either way was because John Henry Eden and Autumn are taken out of the picture either way.
Even then, the ONLY reason the Brotherhood of Steel won at Adam's Air Force base was because the Tesla Canon wielding LW annihilating the lion's share of their Power Armor wearing troops.
As for Fallout tactics, I think the ending without the Computer works best.