For me this is a no brainer for your purposes. I'd pick the 270 Win. Will cleanly take any of the animals on your list and shoots plenty flat, easier to find ammo than the 25-06, and won't smack your shoulder as hard as the 308 or 30-06.
I've taken game with all but the 25-06 and the 270 never ceased to impress me at ranges from "in my face" to over 400 yards.
That is my opinion but the final decision is up to you. Choose something that you are comfortable with and have confidence in. Either one will suit your needs.