The main advantage of the 30-06 is that ammo can be found almost anywhere that ammo is sold, espacally that outback country store. They won't have 35 Whelen or 350 Rem. Mag, usually. But those big medium 35's have a big frontal area, and In my experience I believe that game (at least at medium and short ranges) gets hit harder, and goes down quicker. I will throw the .348 Winchester in there too.
At anyrate, this debate will never get settled, I own and hunt with .308wins, 30-06's, 350Rem mag, and the 348 win, as well as the 45/70 and even the 450 Alaskan in an original model 71.
Which gun gets used the Most by me? For me it's the little .308 Win, mostly because it's chambered in an older steel framed BLR. I like the rifle better for general use, so I accept the caliber it's chambered in. And In reality, I can't recall a single time that I though it handicapped me, as opposed to using one of the other rounds.
If you have the money and time to play with several guns, and you have opportunity to hunt some of the bigger game, then by all means, have at it. If you're just hunting deer, and you only what to buy one rifle or two, then get a .30-06, .308, .270, etc in a rifle you really like and you're good to go.
