Basically- One is a galactic civilization. The other is a one-corner-of-the-galaxy civilization. The former has more ships which are also bigger, more people, more industry, etc.. The latter has a lot of cool techs, but a lot of them don't apply much to a fight.
So yes, the Empire's stronger.
Taking universes as a whole, the energy beings throw things in the Trek corner, obviously.
Also, going back to Empire vs Federation, the TNG/DS9/Voy/etc. era Trek loses, yes... but, interesting, The Original Series and Star Fleet Battles (an EU made entirely based on the original series and animated series), do not. Why? Well, they fight at warp speeds, strafing targets without ever leaving warp (you think hitting starfighters is hard? Imagine trying to hit a target that never slows down to the speed of light), and a single ship is supposed to be able to devastate a planet.
That's right, early era old trek > late era trek in fighting power.