Would a Federation warship like the Defiant out gun a Star Wars Star Destroyer? Who has a bigger armada? Who has the tactical advantage? Don’t forget that The Federation includes the Klingons, who love warfare and have fast, agile, heavily armed ships, with cloaking devices, and the Vulcans with superior logic and tactical planning.
At a glance, it seems like the empire would win on sheer numbers but on the other, it kinda seems like the federation could win if they started doing stuff like beaming empire bridge crews into the sun and whatnot.