What is the best run animal in Sonic Adventure 2 Battle

This really depends. Both the cheetah and the rabbit grant a Chao a 40% increase in run experience. In this case, you'd have to look at what else you'd gain and what you might potentially lose in your Chao between these two animals. The cheetah will also grant 8% experience in Power, but will penalize your Chao 8% each in Fly and Swim.

The rabbit, on the other hand, grants the same 40% Run boost as the cheetah, but will not penalize or boost your swim, and increase Fly by 8%. But if you wanted your Chao to be good with Power, the rabbit will penalize it by 16%!

For most races I would probably actually go with the rabbit, since flying and swimming are usually more important than power, which is only really tested in a few races per category, but good flying and swimming combined with high running scores will get your Chao ahead, and in some cases, a good fly trait will decrease the amount of time your Chao will have his Power tested.