Each are very close, depending what you want to hunt. Other than that, it pretty much comes down to personal preference. Which one would you prefer to own? What type of hunting do you most expect to do? If Elk, Moose or big bears are in the future, I would suggest a hard look at the .30-06. If you're only going to hunt medium sized game, then either would work well.
You do have the availability of heavier bullets with the '06. The .280 closely approaches the 7mm Rem Mag when reloaded. The .270 has a reputation of very flat shooting. Whether you reload or not, the '06 probably offers more bullet selection. The 180's and above tend to have a bit more recoil in the '06. Ammo for the '06 and .270 are less expensive and probably more available than the .280.
I have each in a Handi rifle. The .270 is a synthetic model and is very accurate with Win. 130's. Recoil is very comfortable. The .280 had a 26" bbl and is scary accurate out of the box with Rem 150's. Again, recoil is comfortable. I've only shot 180's out of the .30-06. It was not as accurate as the others out of the box. But its on the money now. Recoil is noticable, but not offensive. However, it recoil's less than my Mossberg ATR but not as much as my .30-06 700 BDL with the same ammo.
Good Luck!
EVOC ONE