No lack of advice and it's all good with some personal preferences thrown in. I've hunted considerably with rifles chambered for both cartridges--your question does not present a dilemma because as has been said both cartridges are elk-capable and easily so assuming you can put the bullet through the lungs/heart at a reasonable angle if other than broadside.
If this is a hump-it publc land hunt or any kind of mountain or higher altitude hunt, my preference goes to the lighter weight rig, assuming most of the other scope/rifle features are equal or nearly so. I think the 250-grTTSX gives the 375s more versatility yet and they haven't been bad in that department before.
While the 270 B will shoot some flatter it's not that much of an issue at "normal" ranges. A 150-gr at 3200 or a 160-gr at 3 grand is pretty darn flat and a 140-gr at 3200-3300 fps very much so. Some like the 130's in the 270 B but I would go just a bit heavier--just a personal preference. But as said, that's not too much of an issue up to 500 yds because a broadside bull or even a cow gives you a 15-20" "dinner plate" target. And a 250-gr TTSX, my recommend if you hand load the 375, should easily be started at 2900 fps out of 375 and it will fly plenty flat.
The biggest factor is neither cartridge or rifle (within reason) but you. Make your choice and then practice from field positions at distances up to the max you are comfortable with. This will build confidence with the knowledge of the trajectory at any reasonable distance with your choice of rifle and cartridge.
Most of all relax; you don't have to over think this stuff. There are a bucket full of cartridges that will kill an elk. You are the most significant link in the chain.
Enjoy the ride.
