Your bullet choices are the widest possible so you will find one that works well for each mission.
True, but there is a ridiculously wide variety of bullets available for the 6.5 as well, from 85 grain varmint bullets to 160 grain solids.
I would not be at all afraid to have a 6.5 swede as my only rifle in North America.
A disadvantage of the 6.5 is that the .264 bullets tend to be a couple bucks more expensive than a comparable .308, but the .30-06 also uses higher average powder charges per round, so you will get an extra ~15 rounds out of a pound of powder. .308 bullets in my experience are also a little easier to find locally, the same goes for .30-06 ammo and brass.
Really, it is kind of a wash between the 2 in my opinion, although the .30-06 would be a little better on larger game.