RE: 30-06 vs 308
The .308 Winchester and the .30-06 are so similar that either will serve you well (did you say "coastal brown bears?") My advice would be to go with the .30-06 because of bullet weight.
The .308 and -06 perform nearly equally from 125 grains - 180 grains (the bullets are the same after all). At 180 grains and up though, the bullets must get longer and to be positioned for correct overall length must be set back further into the case mouth...not a problem with the -06...room to spare...a big problem with the .308 no room to spare (you must reduce the load or go with a more compact powder without effecting pressure). This is where the -06 is better.
If you are serious about including the big browns and even grizzlies, consider something larger(I personnally prefer an Abrams main battle tank)...except for the availability of ammo (and the $$$) the .300 Remington Ultra Mag with power level ammo (III = -06, II = Win Mag, I = Ultra Mag for the big nasties) is very versatile.