At the TNG reunion in Toronto, Michael Dorn was asked why he thought the TNG cast was so close but the other casts weren't. He had an interesting answer saying that when TNG started, with the exception of Patrick Stewart, they were all around the same age, they were all single and none of them had children. So they all were sort of at the same stage in life, and for most of them this was their first real break. So it may have been more of the commonalities that brought them together.
The DS9 cast was a mix of ages, most were married with children and most had careers that stretched back a little so the attitude on set was more of lets get this done and get home.
As for Voyager, I think they all got along well enough until Jennifer Lien was let go and they brought in Jeri Ryan. Kate imploded and was furious about it for the rest of the shows run. The rest of the cast, particularly Robert Beltran, got bitter at their lack of screen time or character development.