When the timeline split, Starfleet started building bigger, more powerful ships. Constitution class is now the size of a galaxy class starship, and a lot more powerful than the original. By the time of the Dominion war, imagine what ships starfleet will have, imagine a JJ-verse Galaxy class... it will probably be the size of a planet. But on the other side of the wormhole the divergence won't have had any effects, so they will have the same original ships etc, in fact even species that were not yet contacted like the cardassians should be the same. So assuming the wormhole is discovered around the same time, the dominion will probably be a complete non-threat to starfleet.