.30-06 advantages: Heavier bullets, slightly more energy, very common, can be used for bigger animals than .270, wider diameter, surplus ammo available if you want cheap bulk target ammo.
.270 advantages: Higher velocity, less bullet drop, flatter trajectory, good ballistic coefficient, some say less recoil than the '06 (but I still have yet to notice recoil from both calibers), very common.
.30-06 disadvantages: More bullet drop, not as flat of trajectory, some say more recoil even though recoil from an '06 has never bothered me, more compatible calibers for reloading, slightly less velocity.
.270 disadvantages: Slightly less energy, not as compatible of a reloading caliber, not as heavy of bullets available ( Woodleigh does make a 180 grain .270 bullet).
I know that there is some stuff I failed to remember to list.
I own both calibers in totally different guns. I like both of them alot but keep in mind that these calibers use the EXACT IDENTICAL BULLET CASING CARTRIDGE. The only difference is the neck diameter for the bullet diameters. .277 diameter for the .270, .308 diameter for the '06. Other than that these are identical rounds with nearly the same ballistics.
The .270 only beats the '06 with less bullet drop and higher velocity. In all other regards including the '06 is a winner. But both are excellent calibers.