I would say .270; flat-shooting, easier to hit with at longer ranges, 150 grain projectiles will take up to elk pretty regularly, yet smaller weight bullets for pests and such.
Faster and flatter than the comparable .30 cal cartridges, generally, equal or less recoil, and bullets of equal weight and comparable shape will have superior SD's and BC's than the same weight in a larger caliber.
The .30-06 will push a 150 grain marginally faster than a 150 in .270 but
a 150grain .277 cal bullet has a similar SD to 185grain bullets in .308 caliber. And comparing 150's in both calibers, with similar profile shapes, the smaller caliber, .277 will generally have a longer more aerodynamic shape, giving it a better ballistic coefficient, reducing wind drift, and allowing the bullet to maintain it's velocity over a longer range, making it flatter and faster, therefore maintaining more energy.
If you handload the .30-06 will have more bullet choices, but 6.8mm bullets, are by no means skimpy in selection. I have seen bullet weights as low as 75 grains in .277 and as heavy as 180 grains. (apparently there are some 200grain bullets in .277, but they're extremely limited)