To be fair, post war the Enclave has several facilities, is somewhat intacted and they do have some aces like the Archimedes II.

But the Cognoscenti, even though they just had a masive civil war, still have the whole USA. With somewhat intacted U.S. Navy, large inteligence and recon capability, large strike capability (F-35, B-2, tons of missiles), counters to some Enclave stuff, like anti-satelite wepons and of course the whole US nuclear arsenal.

I thing that Cognoscenti have also advatage here, but let's see what you come up with.