Federation wins, by far, even with hyperspace technology, that would be no match for the spore drive. But, this all depends on what you truly want to factor in:
1) Which era of Starfleet are we using?
2) Are we limiting this to standard fleets and equipment?
3) Does it take place in the Milky Way or the Star Wars Galaxy?
If you want to use all shows and movies for canon Federation without restrictions, then both the Expanded Universe and Disney-canon have little to no way of winning. A much closer way of the Empire winning would be if you pit it against a 22nd century fleet in a random location in space.
Thanks for the reply Ninja!
Spore drive is strange, fast, and... strange. It is also limited to one ship, and not referred to at any point after Discovery's disappearance. Every other Federation vessel is limited to warp drive, which cannot remotely match hyperdrive for speed and strategic flexibility.
To answer your questions:
1. Post Dominion War for the Federation. This would represent the point where the Federation was still technically on a war footing. For the Empire, The Empire Strikes Back. A lot of Star Wars fans I know who've taken part in these discussions consider this to be the Empire's peak.
2. The Federation has access to all its resources and fleets, as does the Empire. In terms of 'standard', well, I guess that needs refining. Are we talking no 'one-shot' technobabble devices? Ideally, yes, as they usually appear only once, and are never referred to ever again, making them unreliable for debate purposes.
3. Think of it as 'the Empire is invading the Milky Way by means of wormhole'.
As for who would win an outright war - consider that circa A New Hope, the Empire controlled one million star systems (canon, as per the movie's novelisation), and had the industrial capacity to build, in secret, the Death Star, a piece of incredibly advanced technology that, in sheer volume terms, would be the equivalent of building thousands of Galaxy-class ships over twenty years.
In terms of fleet strength, the number often banded about for Star Destroyer numbers is 25,000, though I'm trying to find a source for that. Given that the Empire controls a galaxy via means of dictatorship, it's not surprising they would have a fleet to impress and terrorise the galaxy into submission.
The Federation is harder to pin down. To defend earth against the Borg at Wolf 359 they could only gather 39 ships. The gathering of some 600 ships (the result of two combined fleets) in DS9's 'Favour the Bold' was considered to be a large fleet by Weyoun. 2800 Dominion reinforcements were considered enough, added to existing Dominion fleets in the Alpha Quadrant, to decisively end the war. Yet there is evidence that later on in the war, the Federation fleet had dramatically expanded to several thousand vessels (still below the fleet strength of the Empire).