From a rolling start under 10 mph, the Crossfire would definitely jump ahead, the S just doesn't have the torque to move it at low RPMs. If you were to pull up to one at a light and he started to rev the thing like a swarm of angry hornets, then watch out.
Regardless of which is faster, the S2000 looks like a Miata on steroids i.e. feminine. If you ever want to mess with someone who owns one, just tell him how "cute" his car is and watch him turn red