The NCR will be more organised and cohesive in the New Vegas Area as it is their territory and they know it well, but come on the Brotherhood is massive and has supposed links to the US military, the Brotherhood if they really wanted could Mobilise Troops from several of their operations on both coasts to simply Crush the NCR in one attrition confrontation, but they have better things to be doing and have lsot contact with each other in parts as in Fallout 3, but if there was a full force on full force skirmish with all the NCR and all the Brotherhood the Brotherhood would kick their ass easily, especialy if they had rebuilt liberty prime by the date of 2281 or so considering he was destroyed in F3 about 2277-78 he could be back in action within a few years or 10 possibly depending on how complex he is, with prime the Brotherhood would kick the NCR's ass with only minor casualties, Except the brotherhood would have to seize control of the satelite weaponry of the NCR's in order to prevent their troops getting fried so the Brotherhood would have to stealth in in recon armour with stealth boys, take over the NCR stronghold by stealth and then wait a few hours for the Brotherhood armada of a sort to turn up and finish the job, so yes the Brotherhood would win.-- :foodndrink: (you can Breath now!)
There are alot of "What if...?" in your post. In fact, it consists entirely of them, and you are making crazy assumptions to try and twist the situation in favour of the Brotherhood of Steel.
Fact of the matter is, they already lost one war with NCR, and it's not very likely they'll be able to win another. While the BoS do generally have more advanced technology, their numbers are dwindling constantly, while the NCR has a virtually inexhaustible supply of new recruits.