There have been a number of good recommendations made! Personally, if I had either a .270 or a .30-06 I wouldn' t buy the other for another whitetail/coyote rifle. (And I have owned both of those calibers at the same time....so much for following my own advice.)

Until you get to bullet weights above and over 180 grains in the .30-06 there isn' t enough difference between those two cartridges. For deer/coyotes you will be using bullets less than that, (though 180 grains in the .30-06 can be put to good effect on deer in some applications). Essentially for either deer or coyote you would never be able to tell any difference between a .30-06 or the .270. Now having said all of that.....if you just WANT IT that is a good enough reason!

If I were really looking for another rifle to compliment that .30-06 and the focus was on deer and lighter game...I' d look for something enough smaller to be truly useful for coyote but still useable on deer. I' d probably start looking at something in the .243 Winchester range on the small side....and stop with something in 6.5mm, (such as a .260 Remington or a 6.5X55). In between there are a number of really good quarter bores...such as the .25-06, (or even the .257 Roberts/.250 Savage on the smaller up to .257 Weatherby on the larger). You might even want to give a good hard look at the new .243 WSSM. Which is essentially just a .243 Winchester about 200 fps faster! Though it does look like a promising long range medium game cartridge.

But when it is all said and done....if you just WANT a .270 Winchester....it is a great cartridge!

Good luck with your decision!