150g bullet at 3,000 fps = .30-06Spr. Hornady 150g SST out of a 24" barrel has a PBR +/- 3" from line of sight of 290 yards on deer size targets.
.270 Win, 140g Hornady SST, ~3,000 fps, PBR +/- 3" from line of sight to 300 yards on deer size targets (dinner plate size kill zone).
The .30-06 offers a wide range of bullets, excellent barrel life, ammo availability about any place on the planet. Easy to load for, wide range of suitable bullets and powders, can be shot with out a muzzle brake
on rifles easy to carry. Lot to like about that cartridge. You can say the same for the .270 though it may have somewhat less barrel life - it's still easy to find ammo and is at least in the contest for best deer cartridge on the planet.
Either one of these good old cartridges will work fine on the specified game at the ranges of interest. Nothing exotic. Work real fine, last long time, no muss, no fuss, meat in the freezer.
There are more exotic cartridges that will do the job but they extract a penalty in barrel life and availability I don't like to see in a hunting rifle, and they don't do it enough better to be worth the hassle. But that's me.