What if instead of the Empire it was the CIS and the Republic joining forces at their peak? Lose the Death Star but you have the full jedi order, Chancellor Sheev and Dooku, the clones and all the droids. So tons of resources with competent military leadership and battle hardened fighters.
To me it seems like SWs only chance is to zerg rush out of nowhere and bomb all the main Trek planets with their full might before they can adequately respond with their slower warpdrive travel. I just don't know how feasible that is.
Yeah, a big part of this is also how much either side knows. If the Empire was just instantly transported across, I feel the Federation would have the "home field" advantage there given the fact that undoubtedly an Empirial ship would appear within sensor range of the Federation if not visual range. They'd immediately know what's coming and the Empire would have no idea where anything was in the Federation.
Now, if they were somehow invading from OUTSIDE the galaxy and therefore had the opportunity to study the Federation, then the zerg rush tactic might actually work since they would know where important planets were. This still might not help though as presumably their investigations would tip off the Federation and definitely Section 31.
I think the Empire only really stands a chance if the situation were reverse and the Federation is transported to the Empire.