I like the 270 a lot (family has an old Sako). However, getting it to shoot accurately for target shooting is a challenge. Fine hunting gun.
As for recoil, with your choices its pretty much a moot as you can get a recoil pad that eliminates that as a concern (either on the gun ala Limb Save or built strap on pad).
I have shot the 270 and the 30-06 side by side and really cannot tell the difference. Weight may be a factor as the 1903s we shoot are heavier. It certainly will be in any gun you shoot.
Once you go past 300 yards you still have to hold and its a matter of 2 inches high or 3, or 3 inches high or 4. Until you get way out there is a moot I think and then its really gets interesting.
I am fond of the 30-6 as its versatile. You can run rounds down to the 130 270 common size. Newer powders allow more performance with same pressure (and Hornady is loading some full up rounds that do a bit better as they re factory controlled.
You can hunt Grizzly with it in the 220 gr size (far more of those taken with a 30-06 than anything else). Prime choice for moose and elk.
I wold go 30-06 but not sure why the AP is an issue.