You asked ... my answer 308 Win. But no arguement from me that either would be a good choice for deer sized game.
While there are many comparison points that can be (and have been) made, the top two in my book that put the 308 Win. out front are the 20% - 25% larger diameter of the wound channel and the penetration (i.e. down range "ummph").
It is going to be hard to beat the versitility of a 308 Win. for up to medium large game when using a quality 165 gr. hunting grade bullet.