The empire would clearly win as it has massive military and is a huge threat to the UFP,but thats why its will also lose. Star trek films are made for the enterprise to go against overwhelming odds like saving earth by going back in time without a time machine to bring back extinct whales. If the protagonist is starfleet then the empire will lose again by inferior forces because star trek is about hope and optimism.
The Empire would win because they would be willing to use end-game tactics and the Federation people are pussies in comparison.
The Empire would park either a Superdestoryer or the DeathStar itself next the moon - threaten to destory it - do so anyway as a show of force - demanding that the UFP immediately surrender. And then they would.
Despite any technological differences between the two universes - that the Empire is willing to take any measures to win, means they would whereas the Federation would be hampered by its morality.
A real world comparison would be if the United States threatened to nuke any state that killed even one of our soliders and followed through on that threat would mean we'd win.