I believe the .270 Winchester generally is capable of outperforming the .25-06 both in trajectory and wind-drift and should in theory have a little bit better barrel life.
Similar velocities, pressures and powder type/capacity. Barrel life will be about the same. Having said that, I don't know anyone who's shot out the barrel in a hunting rifle.
The .243 also outperforms the .25-06 in terms of trajectory and wind-drift and has a better bullet selection available. 6mm is a very popular target caliber, so there are some excellent match projectiles available for the .243.
The .243 shoots a lighter bullet at lower velocities, so it will not buck wind as well and will drop faster. Also, .244" pills run 55-100 grains, .257 bullets are 75-120 grains; (I don't count match bullets, like the 107 gr. .244 since OP intends to hunt or bullets to light for caliber, like .257" slugs intended for .25-20 and .25-35), so the spread is basically the same, but the .25 caliber bullets are simply better suited to big game animals. Using the heaviest bullets, .244" and .257" have nearly identical BC and SD, but the .25 caliber slug is still heavier and still going faster, hence more oomph down range.
.257 is just not a caliber known for particularly good BCs, and it shows at longer ranges
The most widely used hunting bullet in the .25-06, the 117 grain Sierra Gameking, has a BC of .410. That's not too far from the .430 of the 100 grain .244" pill, and the .270 only pulls better number with the 140 and 150 grain loads.
If we really want to base what we buy on trajectory alone, we should all be selling everything we own and buying .408 Chey-tac rifles. Fact is, for the OP's purpose, the .25-06 will perform very well. It is a better medium and big game cartridge than the .243, and better suited to varminting than the .270.
If you really want a hot little number, check out the 6mm Remington.
I agree that the 6mm is a great little cartridge, but unfortunately is all but dead outside of competetive shooting these days. I love mine, but I'd never recommend the cartridge to someone who doesn't handload.