I have both and I will always go to my .30-06 over my .300 Win Mag every day. If you ever hear "you need a .30 cal magnum round to kill an elk" walk away and ignore it. You don't. A .30-06 will kill ANY north american game animal and has the largest selection of bullet sizes available. You can get or load 100 grain bullets for varmint hunting and up to 220 grain bullets for grizzly bear and moose. Plus, the recoil is way easier to deal with on a '06 than Win Mag. Yes, a .300 Win Mag shoots "flatter", but don't let anyone tell you that you can't reach out with a .30-06. Springfield 1903s chambered in .30-06 were the ORIGINAL 1000-yard open sight rifle and are still capable of accuracy well beyond that (not that I condone 1000-yard hunting shots, especially with open sights).
Don't get me wrong, I love my .300 WM, but if you truly want a rifle chambered with an all around cartridge, .30-06 is your best bet. If you get into (or are into) reloading, I can share my best recipes for .30-06 hand loads. Good luck!