I assume this is a question based on camaraderie and not just an overall comparison of the shows.
I agree that the TNG senior staff characters, especially early on, could come across as very stiff. But I don't think that holds for later seasons. Sure, you had Picard and Worf who were more aloof and distant, but overall the characters were pretty tight-knit by the later seasons.
Voyager tried to have an early DS9 feel to it with the characters, with them not getting along and the Starfleet vs. the non-Starfleet interests. But they dropped that early on in favor of the "we're all a big family" theme, which was just not very realistic considering their being stranded and split between the two crews.