I read your OP where you want to hunt anything from deer to Canadian elk. I visit another forum that's dedicated to big-game hunting with most participants hunting elk and the *most* debated subject there is the "best" elk cartridge (if there is such a thing....).
An '06 will definitely get the job done and with it's greater case capacity (over the 308) and that it's available over-the-counter everywhere is probably the "better" cartridge (of the two you listed). However, a humane shot taken from an '06 on an elk should probably not exceed 300-400 yds which is also probably the maximum distance any but the most intentional marksman should ever attempt.
I have a 7mm Rem Mag and it gives a little more distance/energy than an '06 (especially so with handloads, but that's another game), but it's not a true, long-distance hammer. In my and in many other long-range shooting practitioner's opiion truly appropriate big-game, long-range (say from 500yds and out) caliber's *begin* with the numbers 338.
The medium 'magnum' cartridges like the 300 Winny/H&H/Roy/Norma are great (my most accurate rifle to date was a 300 Win) and can deliver some serious energy at medium to long range distances. The next up in the medium caliber magnum's like the 300 RUM/Dakota/etc really start to bring the heat - huge volumes of energy at long ranges, but at a cost: barrel life. These hot cartridges are known barrel-burners.
However, when you say *any* big-game in North America that includes big bears and killing those nasty's (from most reasonably experienced accounts) requires as large a caliber as can be fired accurately and confidently. If the largest caliber you're comfortable with is .308 i'd say don't go for big bear. However *i've never hunted large bears*, but the caliber i'd start with is .338.
An '06 will definitely get the job done and with it's greater case capacity (over the 308) and that it's available over-the-counter everywhere is probably the "better" cartridge (of the two you listed). However, a humane shot taken from an '06 on an elk should probably not exceed 300-400 yds which is also probably the maximum distance any but the most intentional marksman should ever attempt.
I have a 7mm Rem Mag and it gives a little more distance/energy than an '06 (especially so with handloads, but that's another game), but it's not a true, long-distance hammer. In my and in many other long-range shooting practitioner's opiion truly appropriate big-game, long-range (say from 500yds and out) caliber's *begin* with the numbers 338.
The medium 'magnum' cartridges like the 300 Winny/H&H/Roy/Norma are great (my most accurate rifle to date was a 300 Win) and can deliver some serious energy at medium to long range distances. The next up in the medium caliber magnum's like the 300 RUM/Dakota/etc really start to bring the heat - huge volumes of energy at long ranges, but at a cost: barrel life. These hot cartridges are known barrel-burners.
However, when you say *any* big-game in North America that includes big bears and killing those nasty's (from most reasonably experienced accounts) requires as large a caliber as can be fired accurately and confidently. If the largest caliber you're comfortable with is .308 i'd say don't go for big bear. However *i've never hunted large bears*, but the caliber i'd start with is .338.