I do recall Robert "Chakotay" Beltran making comments to the effect of how the TNG cast were more of a family, but that the VOY cast simply didn't bond like that on their set. There was certainly more tension on the VOY set, even if it never did spill into outright hostility. And certain cast members, particularly Robert Picardo, seemed to have got along well with everybody.
My recollection from an interview somewhere was that Beltran seemed to resent how the writers gave Picardo so many good storylines and things to do.
If I got this right, Beltran was told that "the Doctor" was getting good material because Picardo would come up with ideas himself and pitch them all the time. And Beltran complained about it, essentially saying "that's not my job" and you should be coming up with better things for me to do.
I found it ironic that when they finally had Chakotay carry an episode, it was that terrible boxer illusion/fantasy/metaphor story which for me was by far the worst show of the series. They gave him an episode, but it was a boring and murky story that no one could have carried off-- except possibly Jeri Ryan, who would have shined in the topless scenes.
Re: Beltran, I remember this being the case as well. Both Beltran and Wang seemed to be the most vocal detractors of their experiences with the show, always wanting more dialog and episode directing opportunities, seeing that some of the others were getting it.
Yeah, DS9 was an odd duck. I do remember Dorn's comment about it being a more "grim" set, but I wonder if that was more of a function of the subject matter of the show (always being promoted as the "darker" Trek) or one of the actors.
I do recall Brooks being the most aloof of the group, however, IIRC, he was also said to have frequently advocated for the other actors to get bigger roles in the show where it made sense to the plot. That, to me, speaks volumes of the man's professionalism and proof that he wasn't about stroking his own ego, despite his top-billing status.
TNG and Enterprise seemed to have the most camaraderie that I could tell, with everyone pretty much having fun with the gig in general.
And yes, top marks for TOS being the most fraught with cliquey behavior and petty squabbles. The "big three" may have gotten along well with each other, but the venom from the second- and third-tier folks, whether perceived or real, coupled with the almost persistent threat of imminent cancellation, definitely puts it at its own level above the rest when it came to disharmony on the set.