I think you have whitetail medicine covered very well. You already own a .30 caliber, so I would go with the 270 Win. Good luck.

I have owned both 308 win and 270 win. I got rid of my 308 and bought 270 win.Flatter shooting.I still own 270 win and wouldn't part with it. You don't need a 308win you got a 30-06 ,which is better.

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Heads 308, Tails 270. Good luck.

There is not enough difference between the .270 and the .308 to squabble about. In fact you can throw the .280 and 30.06 in there too! They are all pretty close ballistically. With what you already have, you would need to go smaller, (.22/250 .243, 25.06, or .260) or larger, (.300 or .338) to make a difference.
I have not mentioned the 7MM/08, it could just be the best whitetail caliber around! It would fall in with the .270, and .308 bunch, but with less recoil!
For a real diference in your collection, a .35 Whelen or 45/70 would be nice! Good luck!