I'd have to take the middle ground on how powerful the Dominion was.
I wouldn't say the Dominion was vastly
more powerful than the Federation, but at least earlier on, the storyline suggested they were more militarily powerful than the Federation-and the Klingons combined.
They were able to attempt to field an extra 2800 ships during the war, which even the Federation admitted that if they got through, meant the end of the war.
Later assesment from Vreenak showed how deficient the Federation situation was in comparison to the Dominion.
The Dominion seemed to be capable of setting up a self reliant system no matter where they were, once the Jem Hadar, White, and ship building factories were in place.
It would have been a replica of the Gamma Quadrant Dominion, had they won.
Problem was, they never really got them into place.
Now, on the other hand, once the Romulans entered the war, the momentum came to a hault.
The ships are spread thin, they're retreating, they're losing planets.... obviously something happened on their side.