I used a 30/06 for a while and the only reason I sold it was because I didn't like the rifle.
In real world terms the 308 and 30/06 are about equal, iirc the 30/06 has around 12% more muzzle velocity when shooting 180 grain bullets of like construction from the same manufacturer.
So what a 308 will do at 200 yards a 30/06 can do at 225 yards.
The 30/06 will also handle higher grain bullets better.
Given a choice between a 308 or 30/06 I would base it on which rifle fitted my better