In most situations I've been in, the bass is a rock while the drummer has a bit more free reign rhythmically. If the bass is draggin/rushing people don't have the support of the bass defining the time. It depends on the situation, but for most that I'm in, the bass is the time where the drums is there chiefly for textures and dynamics. Like big band stuff- the bass is walking while the drummer is doing kicks, fills, punches, etc.
Way off topic comment of the day- What's also nice about being a bass player is that you also get to define the harmony. If a guitarist is playing C, F, G - you can make it into a Db maj7 b5 (or aug 11), Gsus7, Csus, Fsus2, Dmin7, Eb6, Amin7, AbMaj13, etc.