IMHO the 308 is one of the best rounds out there for almost all we can hunt here... its offspring (7-08, 243, 260, and 338f) grew from the 308 case, and they too are just really good cartridges.
As mentioned, its accurate - so are its offspring... it is in use by the 'services', as well as long distance shooting - people who use it know that it can in the right hands shoot a long long way - much further than most deer hunters can shoot accurately.
Yes, its smaller than the 06, but not by much - look at the 500yd drop and the diff is just a few inches, almost negligible...
The only people that don't like this round, or its brothers, are ones that haven't shot it enough to really see the value here.
So to answer the OP question, its an awesome deer round, prob one of the best ever.
And I don't own a 308, but do have 3 of its offspring - and they see 10x more action than the big magnums that are now safe-queens... I can shoot a 260 or 7-08 for hours at the range - can't do more than a few shots with the 300 before I have to focus on not flinching...