Throw in Liberty Prime and partial control over the purifier, an alliance with Rivet City, which might produce quite a bit of stuff eventually, once more people flock to their clean water + 3 years time, BoS could be very powerful around there, especially since they are impervious to the problems of radiation in nuked areas, whereas my guess is that the NCR troops could suffer dearly from that, but I never played the other two, so don't listen to me, lol.
They would still not be up to par with NCR's forces.
Even if they tripled their members they wouldn't stand a chance against NCR.
And Lyons BOS are stupid as hell because instead of saluaging the tech from Crawler and Raven Rock they blew the places up.
They are under-supplied and have lost a lot of member in their war with Enclave, and Liberty Prime will take alot longer than 3 years to rebuild.
And even if they do rebuild it I hardly think it would be the same quality as it was during it's attack on the Satellite Array Station.
I don't understand how it's still a debate.
Do some of you understand how big NCR is? Have you done any research on the Wikia? Played Fallout 2?
Lyons Brotherhood had one ace up their sleeve. Compared to how big the NCR is I wouldn't be surprised if they had at least half a dozen ace's up their sleeves.
The only BOS faction that NCR wouldn't stand a chance against is probably the Mid-western BOS (Tactics).
So let's think this through:
NCR
-Huge army.
-Advanced weaponry (They sold pretty awesome stuff during my fallout 2 playthrough's so I don't understand how people think their weaponry is "decent" at best)
-Unknown amount of secret weapons (One we do know of is Archimedes.)
-Elite force known as NCR Rangers
-Do not have power armors but have pretty good armors non the less.
-Outcasts may very well align themselves with the NCR in order to take Lyons down who in their eyes is a traitor.
-Seems to have a problem with communication (New Vegas)
Eastern BOS
-Power Armors (But NCR has weapons that can penetrate their armors)
-Under-supplied. (As far as I remember they don't have any huge storage filled with stuff and they don't produce any either)
-Liberty Prime is broken.
-Still very selective when picking members. (They wouldn't pick us, the PC's, until BS, if they wouldn't pick us, then why would they pick random people?)
-Outdated weapons (Enclave using plasma weaponry while BOS using small guns weapons and laser weapons)
-May very well be under threat from V87 mutants and remnants of Enclave.
-Has no allies.
So, who would be the winner?
And I am being unbiased in this.
If I'm wrong on something then feel free to correct me. I myself want an answer to who is the most powerful faction.