Sisko is more liable to go crazy at any moment, he gets his hands dirty with his crew.
Picard generally let Riker deal with the disciplinary issues, Riker his Picard's "muscle"
Sisko didn't have a real first officer like Picard had, well he had Kira but she was her own woman and worked "alongside" rather than "with" or "for" Sisko. And Jadzia wasn't the one to deal with that kind of thing.
The dynamic aboard enterprise was different, notice in First Contact Riker had to be not on the bridge when Worf kicked off because otherwise the writers would have had to have him do something.
Notice the symbolism a lot of Riker standing just behind picard, staring. Also note that while Picard is a small, older man Riker is a lot younger and a big brutish looking man.
He's his henchman