The reason the Romulans were originally suggested to be important to the outcome of the war was because they tolerated the use of their space (periliously close to Vulcan and Earth, supposedly, considering the fictional history) for Dominion operations but did not tolerate the Alpha Axis striking back at the Dominion through said space.
The fighting power of the Romulan Star Empire might in fact have been utterly insignificant, comprising just a Potemkine force of a few dozen big Warbirds against the thousands upon thousands of Starfleet or Klingon warships. So the Romulans joining the Alpha Axis changed everything (the Dominion no longer could conduct sneak attacks through the Romulan Neutral Zone), but the Romulans joining the Dominion would have changed little or nothing (the sneak attacks against the soft core of the UFP would continue, even if now the Axis could strike back without having to care about making enemies of the Romulans).
Timo Saloniemi