If by nothing else, the Dominion has the numbers to beat anyone else. Just their small advance fleet, bolstered by the Cardassians, was enough to make big advances at the beginning of the war. Also, unlike Starfleet, the Dominion's big ships are pure warship.
Of course, a big part of the Dominion's wins at various points were due to weapons that the alpha-alliance couldn't counter: first it was just their regular weapons - the smallest Trek ship weapons can tear apart an effectively unshielded, unarmored starship, even a big one like a Galaxy-class.; later it was the Breen power drain weapon. After those challenges were overcome, the Allies were back on the offensive (especially with Romulan support).