This isn't meant to be rude in any way, but if you have to ask, you better choose the .30-06, based on recoil alone. I know WAY too many guys that did the "macho" thing and bought the .300 based on 'crowd' recommendations (mostly guys that have never really hunted, but are experts).
The .300 is not a beginners caliber. It is best served in the hands of a seasoned shooters/hunters that can handle the recoil without flinching. Most guys that buy into the .300 magnum mind thinking can't hit their arse with both hands after 2-3 shots, due to severe flinching. The .300 has a very sharp recoil curve.
No animal is really going to tell the difference between the two calibers. .30-06 ammo can be had at Wallmart for $14 a box. Military ammo is even cheaper for fun and practice. You don't need premium bullets for the .30-06 either. I shoot them both and love them, but I shoot the .30-06 SOOOO much better. I don't have to think about how far away my eye is from the scope when I shoot either. I don't have to worry about uphill shots with the .30-06 to avoid getting cut. I have to really concentrate when shooting the .300 to keep from getting a magnum eyebrow. Flinch
