Could the Federation defeat Star Wars' Empire in an all-out war?
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.
we talking cross universe or cross galaxy fight? Q likely takes issue with someone coming into his playground if we're universe hopping. Galaxy to galaxy it's carnage. As the thread here points out, both can destroy whole solar systems. Sure the federation would be slow to start doing so unless Janeway is still around. But they'd get there. Cloaking and transporter tech can make up for a fair amount of the federation being massively outnumbered. If the empire has to gind through borg territory before reaching federation space, that would balance things out. But really Trek time travels more often than stargate so who knows what madness that leads too. We may discover Sisko founds the jedi, while O'Brian finally snaps and founds the sith after being tortured for the 10,000th time.
Just to pile on O'Brien, have something terrible happen to Keiko & Molly. That should really send him along the path to the Dark Side in an attempt to bring them back.