It is important to remember if one is reading the Vault Wiki or other sources which could establish canon which parts are not canon and which parts are. I looked through the Vault wiki and immediately stumbled upon the "war" pages. Before then, I knew they weren't canon, but I thought I should point out:
The apparent "War With NCR" has been part of the Van Buren design documents, and is therefore not canon. I can understand how one can get this confused with real canon, as the NCR page on the vault wiki does not have the labeled caption regarding Van Burne canon.
With their superior technology, the Brotherhood managed to hold out against the NCR, even coming close to total victory. Yet, the Brotherhood's technological advantage was eventually outdone by the sheer size of the NCR's army; no matter how many troops the NCR lost, they always seemed to have more. The Brotherhood, on the other hand, were still a selective group, and thus, was short on numbers. With this discrepancy in troop numbers, the Brotherhood's defeat was imminent.
The above is based on non canon. Below is based on what is canon as of now.
This is all based on the http://fallout.wikia.com/wiki/Brotherhood_of_Steel page of the wiki. Looking at the http://fallout.wikia.com/wiki/NCR page will also point out the same apparent "war" but it is the same Van Buren non-canon source.
In short, I can understand how one can mix up canon, especially is its not labeled on the wiki.
And last with this, if I recall correctly from playing Fallout 1 a couple of days ago, The Western BOS will allow you to join--provided you do a dangerous task for them. And they'll reluctantly let you join and treat you like an outcast for a bit, however they still let you join them. I think making a person do a trial to prove themselves at the glow is better than random recruitment. But my point is, just because the Mojave chapter doesn't want to let people in, doesn't mean the entirety of the Brotherhood do that.
I would personally like to point out what was said above: the Eastern BOS is severed from the main Western BOS unit, and until true canon can provide us evidence of the Western BOS as a whole breaking down, then one should reach the conclusion that the Eastern BOS is still weaker. They have one place, have half of their units severed from them into the Outcasts, and have a limited supply of tech. In my opinion, both the EBOS and the Outcasts are both doomed.
Again, this is incorrect. The war was based off of Van Buren canon, and the only established canon that has anything to do with an NCR and BOS conflict thus far is the Mojave chapter.
This isn't even in the canon, but based upon your choices. So one can't live this as canon until the canon source proves its truth, in which case, one can't use it to prove any points...its a rather moot point in that sense.
Sorry, I just had to point some of that stuff out because I'm a jerk like that.

I think it would be cool to have Lyons making contact, or one of the old companions like Fawkes. Three Dog would be really strange...
I think the character I would like to see again would be Mister Burke. Flesh out his character more in Sin City, where his character belongs better in my opinion. Or, do something with the Regulators.
I'm not sure though. I'd prefer my Capitol Wasteland to stay out of my Mojave more than anything.