Nothing wrong with either one of the cartridges you asked about, but for what you'll be hunting & where, I'd go with a 270Win. or
280Rem.
Take a look at Remington's model 700 LSS Mountain rifle - stainless with laminated stock. Lightweight, too! It can be had in
270Win., or if you prefer, the 7mm-08.
Here's a link: http://www.remington.com/firearms/centerfire/700mtnls.htm

I have one in 270Win. Very accurate. One of the other folks on the forum here, I believe he goes by the handle of "Firstshot", recently acquired one in 7mm-08. You might want to do a little search on it. He's posted several comments/targets, etc.