I like the 7mm better than the 06 too, and i've shot deer, caribou ect. with both calibers. The 7mm will have a bit less recoil, and in this case, the 7-08 will come in a short action gun instead of a long action the 06 comes in. (assumeing your talking bolt action guns)
Both are excelent, but for deer-blk bear sized game, the 7mm would be my choise just because of the lower recoil.