Both the Savages and the Rems that you mentioned are available in cartridges that are better suited than the .308win.
Not that the .308 is bad but I'd much rather have a 300win, 300WSM, 7STW, or whatever if I was buying a new rifle for shooting biggame at extended range. The larger cases are much more capable of getting the heavy/hi-BC bullets up to a reasonable speed.
Either way, Good shootin'
VH