There isn't an elk alive that can' be killed with a .270. As others have noted, Id also suggest a better bullet than a factory Remington. Noslers, Barnes, A-Frames etc... are all available in .270. Pick whichever groups best in your rifle. I mostly use Noslers in my rifles up to 9.3mm and then I use Woodleighs.
That being said, If I has a .338 and a .270 I'd use the .338. While the .270 would be great for broadside shots, the .338 will get to the vitals from any angle. With a good expanding bullet it will always cut a bigger and deeper wound channel. Personally, I like 2 holes in game. It lets more blood out and more air in. But, bullet placement is everything and if you put a .270 bullet in the vitals it will kill the elk Everytime.