One thing the .308 can do that the .270 can't is shoot the same weight bullets at the same muzzle velocity, at slightly lower pressures with less powder. This results in somewhat less recoil, around 20% with 150-grain bullets according to the basic recoil-energy formula.
John, how I think of recoil between different calibers is not to compare bullet weight, but to compare Sectional Density... I think that's a more fair comparison. So, in the case of the 270/150 gr I think the more fair comparison is the 308/180 gr (.279 vs .271 SD). In this case, everything else equal, recoil is essentially equal.
Regardless, what one will do, the other will do. At my core, I'm a 308 guy. Have three currently and no 270's, though I plan to rectify that.
