That's a good question. Been a while since I've done this sort of thing "in anger", in fact way too long, but i think it will depend a bit on the type of music you play. For straight up rock, say, you might be inclined to stick with the drummer, for jazz your rythmn might come together with the other band members at some point during the song ;-) So the norm would be the first option, with the second option more as and when the song requires it. But hey, I'm out of practice, as I said.
*Stands back ready to be shot down in flames!!*
Cheers,
Russ