I was in a position similar to your's not too long ago and opted for the .308. Here's why:
If I need a heavier bullet than the 180 grain I'll get a different caliber. The 30-06 will take down, with good shot placement, any large game animal in North America. The .308 is close on it's heels but I would prefer something larger of caliber or flatter shooting than 30-06 for Bison, Moose, Bear. That means I need another rifle for those game animals.
Everything else can be taken with the .308 and I'd venture that if forced one could take any game animal with the .308 that they would use the 30-06 for. As noted the .308 is abundant. The 30-06 was the "do it all" round for hunting if one was going to have only one rifle. I'm not constrained by only having one rifle so it's not a factor to me.
If you are hunting deer and antelope I would think the .308 is plenty heap big medicine. Those seem to be the most commonly hunted large game. Elk and moose, as well as bear, don't seem to be hunted as much by the "average" hunter. Within it's capabilities and range you can also do well on moose and elk, but I find other calibers better. I also like that the .308 is a bit flatter shooting, think bullet arc from barrel to target, and the shorter action is quicker to chamber another round without raising my head from the stock on a bolt action rifle.
I suggest you consider the game animals you will hunt most frequently and select a caliber that is sufficient for that. If done properly you will most likely have a caliber that could be used in a pinch on the larger species of game you would hunt but it may not be optimal. There must be a reason Col. Cooper selected the .308 caliber as a general purpose rifle out to 300 Yards for hunting. It may not be optimal for all conditions but it will do in a pinch.
That's my $0.02.
Biker