Here are some of my thoughts, off the top of my head:
*We might not have the Borg since Sisko wouldn't have taken Q's crap after Farpoint.
Which brings me to:
*Q wouldn't have shown up much after Farpoint.
*Jennifer might still be alive, since there possibly may never have been Borg....or at least they would have shown up later rather than sooner.
*Picard would be an entirely different person after dealing with Dukat...and the Dominion War.
*It would have been interesting seeing how Wesley and Jake would have interacted....if they did indeed interact with one another.
*Would Picard and Dax been an item? Or would Picard eventually end up with....Kasidy Yates?
*Sisko is by-the-book, but he's not a hard-ass....and, on the other hand, he is not entirely laid-back. It would be interesting to see how Riker adapted to his commanding officer.
*Picard as Emissary? Would Kai Opaka see that in Picard's pagh?
*Sisko is a thinker, and is very clever. Would he have need for Guinan? Or Troi? (I think for either women, he would have tried to get them to tell him more than just 'surface answers' or riddles, or the obvious when their counsel was needed or requested).
Bringing me to:
*In 'Generations'....I think Sisko would have sat down, had a long chat with Kirk....returned to 'normal' time when they first met Soran and arrested him....then talked to temporal investigations on why that arrest happened.
*Worf wouldn't have been all jumpy in the first season; Sisko would've calmed his ass down.
*Data would have found Sisko fascinating.
*Sisko would have found the dark-skinned Ligonians fascinating.
*Picard would have to 'step it up' since Quark would feel he is too soft in earlier seasons. Of course, Odo would be the same watchful individual.