Simple...
Darth Vader can only be killed by Luke Skywalker.
Therefore, the Empire will walk through the Federation easily,
However, they will be unable to kill the main characters, BUT they can still conquer the Federation- only capture Sisko, Picard, etc, not kill.
Then Darth Vader will subject them to interrogation
Following that, they'll escape, and Sisko will make some speech on the horrors of war while Picard whines about the old days when they were explorers, not warriors.
They'll find some way to get to the Enterprise and Defiant, then beg to Q to send the Empire back. Finally Q will make Picard beg on his knees, then snap his fingers, and Darth Vader will wonder what he's doing back on Coruscant. Unfortunately the Federation will have been wiped out, but Sisko will return to DS9 and Picard will keep exploring with the Enterprise, and not have to worry about bothersome Starfleet Admirals.