I have worked woth a lot of drummers, but only 2 for any length of time (as in 5 years for the first, and 2 years for the second).
Firstly, both were what I consider to be very proficient and "musical" drummers (if you know what I mean) - not just bash it as hard and fast as you can.
Drummer A was what I would call "loose". That's not meant as a bad thing - he could (and would) play slightly ahead or slightly behind, and by locking in with him there was a nice tension that created a groove. Hard to explain, but I'm sure you at least kinda know what I mean. He would speed up and slow down slightly during songs which I found difficult to start with, but after a while I got used to speeding up and slowing down with him almost unconciously. I only really noticed it when listening to live recordings back with click track, but it sounded tight live.
Drummer B was a technician. He was much more schooled than A and could run pretty much any style at will, and do all sorts of cool stuff. I was really impressed for a while (and he is still an amazing drummer), but it did end up feeling sort of mechanical, like playing to a metronome. I think it still sounded good, but to me always kinda lacked "feel" (whatever that is), and the connection with him for me was never as strong as with A.
The one thing they both had in common, though, was that they definately listened to the band. Some drummers think their job is to drive it along, but if the rhythm section ain't happening (all of it), then the band ain't happening IMHO.