In my opinion I find the .308 round a great hunting round. There are much more in the ballistic developments in the past 15 years due to military required applications than in years past. Being a NATO round definitely helps keep the costs for munitions lower and readily available. It is big enough to get the job done.
On other notes I also have several other calibers; .270, 7mm Rem Mag, and 300 Win Mag. I find a good all around caliber is the .270 you can hunt and kill any large game animal in north america with confidence. If i was hunting say moose or elk with a .308 I would be very big on my shot placement whereas the .270 or larger caliber would be slightly more forgiving.
Slightly overkill for whitetail or black bear would be the larger 7mm/300 win mag calibers. Though I have a couple to round out my collection I find they drop eastern whitetail like a stone, you don't have to trail anything. On Elk I have found very similar effects. The only thing I don't like with these calibers is that the munition itself is expensive compared to the smaller calibers. I prefer to shoot the animals in the center of the spatula as it gives me a instant audible recognition that I hit good, it devastates the animal usually quick instant kill. The actions on the larger caliber for the most part are quite heavy, so depending on what type of hunt and territory you are in all these factors play a part in your decision.
With that, good luck and good hunting. Let us know how you make out.
Cheers,
Jake