Of the 2 you listed I'd go with the 270 Win. I'm a fan of heavier bullets and it is easy to get 270 with a 150 gr bullet. Plus, as others have noted, ammo is easier to find if you don't handload.
But, if I was picking a rifle for myself for whitetails it would be my Rem Model 700 Classic in 6.5x55 Swedish. I love the rifle and am a big fan of the 6.5mm calibers.