Not a particular fan of the .308 Win. I do own 2 but IMO the 30-06 is much more versatile especially when talking heavier bullets for elk and big black bear. The .270 is a dandy cartridge but not usually all that accurate with the heavier bullets. It shines with 130 grain bullets but in my experience the accuracy drops off considerably as you get into the heavier weights and IMO a minimal cartridge for elk and requires good shot placement.
I have a bunch of rifles by Rem, Browning, and Win but the one that I find myself using more and more is my Tikka T3 Lite in 30-06. This rifle is light, accurate and the bolt is slicker than snot on a door knob. I have it topped with a Burris Fullfield 3-9x with a BDC reticle that works very well out to 500 yards.