With their defeat of the Enclave and reactivation of the Purifier, recruiting will be through the roof as glory-seeking individuals join up, while the large stockpiles of Enclave tech they've seized will enable them to move effectively against the raiders and mutants of the Capital Wasteland.
Now that they have Vertibirds and APA MkII, I can't see the muties or raiders remaining as a real threat for much long; the raiders are liable to simply move on as the Brotherhood exerts its power (you can't beat a vertibird and most raiders don't want to pick fights they can't win) while the mutants can be crippled simply by sealing off Vault 87 with a vertibird strike.
It'll be touch and go for a bit, sure, but the advantages of APA MkII, Enclave energy weapons, a steady recruitment base and most of all Vertibirds cannot be understated. They have lethally effective air support that none of their enemies in the Wasteland have any counter for.
I'd say that by the events of New Vegas the CW as we saw it is likely unified under the leadership of the BoS and Rivet City; whether they will be a state subordinate to the BoS or equal partners with them is hard to tell, though.
Mutants and raiders might still be around, but they'll have been driven to the fringe.
Why none of this high-tech stuff did the Enclave any good.[censored] Bethesda...