I have hunted with the '06 for nearly 30 years now. It has never let me down. It is fully capable of handling anything on the North American continent and most things in Africa (at reasonable hunting ranges). The advantages of a 7mm Mag (or ANY magnum for that matter) over a .30-06 are few. They are primarily two... slightly higher velocities and slightly flatter trajectories. The advantages of the '06 over the 7mm Mag are many... wider range of bullet weights (55gr - 220gr in factory loadings), less recoil (generally), larger diameter bullets = larger holes punched into target, efficiency of powder, availability of factory ammo, different rifles chambered for it, cheaper component costs for reloading, and probably a bunch more that I haven't thought of.
Bringing the .308 into the equation, it can hold it's own against either up through bullet weights of 165gr. Actually, due to it's case size, it is SUPERIOR to the '06 in the lighter weight bullets (efficiency and velocity). If you were not going to hunt anything bigger than deer, the .308 is a great choice. If going after elk or moose, the '06 is the better choice.
My vote is for the '06 as the best all-around cartridge available, with the 7mm Rem Mag a distant 2nd choice. If I needed a "magnum", my choice would probably be to go with the .300 WSM.
Bottom line, though, is really defined by the following question. Which cartridge can YOU shoot most accurately and comfortably? If one has too much recoil, you won't shoot it often enough to become proficient with it. Remember, a well placed hit with a marginal caliber will kill something much more quickly than a miss with a "super magnum".