I'll say it...of those two options, I'd go the 308 route (mostly to be contrary...LOL) but really because I HATE the -06...I refuse to own one...every one I have shot kicks beyond necessary fort the cal and lacks in accuracy when compared to the 308. I have 5 308's in my safe (oddly enough 3 of them are lever guns). I like lever guns, although I don't regularly hunt with one much anymore (to many options in the safe I guess)...not all lever guns are created equal and while I agree that the tube fed guns (Marlin 336's and Win 94's, etc....which I also have a couple of and love for different reasons) have some disadvantages over some of the box magazine fed guns...for which I have 3 chambered in 308 a Savage 99 (my all time favorite rifle to hunt with), Winchester 88 and YUP...a Browning BLR Model 81. They all shoot very well, although the 88 took longer to find a load it really liked and have all taken a pile of animals (including a couple elk in WA) over the years.

As someone else said, lever guns have advantages as do bolt guns...lately I have been more inclined to hunt with a couple of my bolt guns more often, but not necessarily because they are all that more accurate just because I really like the calibers my bolt guns are in right now...

Bottom line, there is no one "perfect" all-around gun (if there is, please don't let my wife know!)...and as much as I despise the -06...both the -06 and the 308 will certainly get the job done you are asking of it.