Lots of things would be different. No Quark and possibly no DS9; at least not as we know it.
I think maybe the Klingons would also be different. The show would have this new baddie to play with and wouldn't revisit some of the older ones that they purposely stayed away from. The Klingons might be full Federation members as suggested earlier on and not revisited except for a couple times when Worf went to see his parents or something. The Romulans might be out entirely too, having only been brought in at the end of the first season when it was obvious to everyone the new Ferengi weren't working out as planned. Heck, maybe we find out Reunification happened decades ago between TUC and TNG, and they're all logical now.
The focus would be this new Cardassian threat, one that was more powerful than the one we know, as it would be a match for a Federation that absorbed the Romulan and Klingon empires. And it certainly seemed scary enough after "Chain of Command, Part II."
If you've got all that, the whole series is different. Would we ever meet the Borg? The Talarians or Sheliak? Would the Jarada and the Breen be more of a thing? How would Q storyline go differently? ...Mirror Universe episode?