Both will do you good. Shot placement is the key factor! 30.06 has far more bullit designs, weights, and styles than you'll ever shoot. I my opinion, the 30.06 is more versital in the over all world. The .270 has great proformance and flat shooting...but over the counter rounds are limited.

If it were me, go with the 30.06.
I'm 5'8" and don't have a problem with the .06....