Wonder how DS9 turned out in that universe, since Sisko wouldn't have become a broken man....
We know that in the same quantum reality that the Bajorans overthrew the Cardassian Occupation and became more aggressive. Unfortunately, that's the only clue we're given.
If the deflector pulse worked, Wolf 359 didn't happen, Jennifer Sisko didn't die. It's possible Sisko remained first officer aboard the Saratoga or became her captain later on.
Additionally, things likely could have gone down a lot different in "Ensign Ro" with Riker in command of the Enterprise without Picard there and the plan hatched up by Admiral Kennely and the Cardassians may have worked. Part of that scenario may have also hinged on how much influence Guinan may have had on Captain Riker during those events since, had it not been for her, Picard may not have given Ro the benefit of the doubt in the original timeline.
The outcome of that episode alone could have affected Bajoran/Federation relations, with the Bajorans seeing the Federation as allied with the Cardassians after Kennely helped them grease a bunch of Bajoran refugees.
This would be an interesting "Myriad Universes" story. It sure as hell would have given the Prophets a headache though.