well yeah you are talking about specific Game Mechanics there...its really up to you and I would only suggest play test both ways and see what works better for your game...
I agree with sqiddster..but like he said ..if its the games main purpose..like a race...between player 1 and player 2...then yeah go for it...
but Playtesting is where its at....find what works best for you..its your game...
and dont forget to consider other options..as well..there are always more than one way to skin a cat...or mouse for that matter...even though they are smaller.
Note:- Under no circumstances does mystazsea recommend the flaying of any animals ...even in a digital or virtual sense...The opinion offered was a metaphor only not intended as a actual option for making games on a computer system...:)