The NCR is alot stronger.
1st: The NCR would have easily won the first battle of Hoover Dam as we learned in Honest Hearts from Joshua Graham. If it weren't for what happened at the Divide.
And if Joshua Graham hadn't made the mistake of chasing the NCR through Boulder City they would've won with ease. They barely had any casualties pushing the NCR off of Hoover Dam.
2nd: The NCR isn't even actively fighting the Legion. The NCR in the Mojave is more of a police force/border guard then an active military at war. Their plan is to contain the Legion not take it out.
They're fighting the Legion in Nelson and recovering in Searchlight from the Legion's radioactive attack there.
Everywhere else is them trying to gain influence so when they take over (because in their mind it is a when) not everybody will be against their rule.
3rd: The NCR is the largest faction in the known wasteland. It goes from Baja Mexico in the south to southern Oregon in the North, and as far east as Reno Nevada. Their greatest advantage, their numbers.
Unlike the Legion the NCR's population isn't mainly focused around their military.
For the Legion there are a few settlements but most of the people are warriors and slaves dedicated to the war effort.
4th: The NCR manufactures weapons and ammo and has doctors that use real medicine.
The Legion doesn't rely on technology. In a war of attrition they would win.
5th: They have howitzers and Vertibirds (where there is one there is more).
They only showed them using one to drop of the president, my guess is they have so few they're only used when absolutely necessary.
6th: This goes back to having a large area and not wanting to fight the Legion. The Government has their best troops such as their Rangers out "chasing ghosts in Baja" and protecting brahmin.
Even when they're brought up for the Second Battle of Hoover Dam the NCR loses without the Courier's help so that counts for little.
7th: NCR has taken out Navarro and is winning against the Brotherhood of Steel, they sent a whole chapter underground.
What was the ratio, one or two dozen dead NCR troopers for every dead BoS Paladin? Numbers wise that's a loss.
NCR is fighting with one hand behind it's back. NCR will win due to higher numbers and better technology. Sure Legion has decent training, but what is this in the face of MGs? A big red mess.
Funny, seems the NCR is going all out against the Legion bringing in the Veteran Rangers and they still lose without the Courier's help.
Once again, almost all of the Legion is dedicated to their armies but that's not the case for the NCR.
Who says the NCR has better technology? Service Rifles aren't nearly as good as Cowboy Repeaters.
Decent training? They have incredible training that you're trying to water down to make the NCR sound better. An NCR trooper against a Legion recruit one on one with no weapons is a cakewalk for the Legion recruit. Don't talk down on the Legion's training when the NCR just teaches them how to pull a trigger and throws them on the front lines.
Guess what? Legion has MGs too. A TON of them, they just don't rely on them like the NCR.
I always hate it when people try to make an argument like that, at best they severely stretch the truth to try and make the Legion seem like they never use guns.