Both excellent choices!
Ballisticlly the .264 will drive 10 more grains at same approx speed as the .270 with 130. So superior BC will shoot a little flatter and drift a little less.
Expect a little more muzzle blast, although alot of .264s come with 26" tubes, so the slightly larger volume pressure wave will have dropped to similar pressures as the .270 exiting a 22" tube.
.264WinMag was the first of a set of siblings(.300,.338,.458) that were perhaps the finest cartridges of the latter part of the 20th century, so there is a nostalgia and mystic factor there, but the .270 is a legend as well, going on 87years young.

The .264 is still very uncommon in the game woods, or a tleast here, so it would make an interesting conversation piece at the camp.
You know the .270 will have a better selection of ammo even at Cambodian Tire, than all the .264 loadings combined anywhere,......that's of course if handloading is not your forte. Everybody gives their best selection for the .270.
For the game you noted in your OP, both a fine choices.
For a quick side by side, apples to apples comparison, use winchesters onlline ballistics calculator,....... select the 140PPSP for the .264(only choice lol) and 130PPSP for the .270. Select a 200yd zero and click "Shoot",..... you will see they are nearly ballistic twins with this bullet choice. I believe both are given with 24" test barrels, so real world will differ slightly in .264s favour, if the .270 has a 22" and the 264 has a 26" barrel.
For classic Rifle/Cartridge combo's, if you are interested in this idea, .....make the .270Win a M70 FWT, or the .264WM in a Mod70XT.