Some years ago, looking for an antelope and mule deer rifle, I settled on the 25-06 Rem. It's an old cartridge, but it gets with the program and gets the job done with very little recoil, great accuracy, and serious lethality.
Are you a handloader? That makes a difference, because I've found that it takes handloading to bring the best out of this cartridge.
100 grain bullets at 3340 fps via H4350. Used that for three mule deer, then moved on to the 115. It worked fine though.
115 gr bullets at 3150 - 3190 via Retumbo. Farthest mule deer with that was right at 400 yards, holding on the top of the back. Coyotes out past that, no problem.
Most of my antelope &mule deer hunting has been done with 115 gr bullets, either the Berger VLD or the Nosler Ballistic Tip. Both are good.
The 270 is very similar, and if you prefer it, go right ahead. Not much difference. Mild recoil. Great accuracy. Flat trajectory, and things fall over very quickly.
Regards, Guy