Well if i had to buy one i would go for the 30.08 it's two points bigger then the 30.06.:lol :lol :lol :lol :lol :lol :lol for real if i haed to choose the 30-06 hands down but both are great cal's .My 2 cent.
What kind of hunting do you do? Are you recoil sensitive? I like the 7mm-08 for deer and the 300 WSM for the bigger stuff. Both of these cartridges are very efficient and intrinsically accurate.
To answer the question, I would choose the .308 as it served me well for many years (untill I wore it out) and meets the above criteria. Both cartridges are awesome and you can't go wrong.
Either/or. Ammunition availability should be a wash between the two. Same calibre so the same choice of bullets. The 06 will have a slight edge in the speed department because of the extra case capacity, the 308 is available in a shorter action. They are both very capable for all Alberta game.
I like the Browning firearms. The two I have are solid and reliable. A little trimmer than the Rugers. I haven't looked at them recently but I was not impressed with the Remington synthetics when I did. The balance was off.