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.
I don’t think you are grasping the difference in scale here. Even if you grant the Federation absolute technological supremacy (which is debatable, but ultimately doesn’t matter). The Galactic Empire at its peak has effectively unlimited resources and the logistical capability to build at unimaginable scale. They could park a fleet the size of the entirety of Starfleet over every Federation world at the same time. Even without superweapons they could devastate all those worlds, lose every single ship in the process and still be able to project power.
Wars are won with industrial capacity and the ability to leverage that capacity. The Empire is perfectly configured to conquer. Their weakness is asymmetrical war from within their infrastructure. The Federation could fight this way, surrender while hiding or scuttling their capital ships, join the Rebellion while bringing significant engineering and technology to bear from within the Empire. That would work.
But a straight-up conflict? No. It’s not a fair fight when one side can absorb losses of any amount and the other side can’t.