Whichever one your local shop has more ammo on the shelf for or whichever rifle is in stock first. Either is a plenty capable chambering, pick the bullet you want to run and whatever it's min velocity for expansion is will be the limiting factor. Most cup and core bullets that's around 1800fps. Either chambering is going to start around 2600fps in a shorter barrel.
For elk a controlled expansion or bonded cup and core bullet is insurance on a shoulder hit. Both chamberings have a huge selection of good bullets available in factory form.
6.5 will buck the wind a little better, 308 will force you to make better wind calls. Difference in recoil will be negligible, difference in drop negligible a couple more clicks of elevation is nothing, cost of ammo negligible. I've killed and seen truck loads of game killed with both no real difference in terminal effect. Both having short barrels you should be able to get away with "match" bullets in either they won't sling them fast enough to hinder penetration.
My 308 loves 168gr a-max and eldm, my 6.5 creed I've only shot 130-147gr no real difference in groups with factory ammo. The 130gr 6.5 has a better bc than my 168 .308 and it starts off little faster.
That being said if you've got a 270 already that's probably a better option for elk, the extra powder capacity will help in short barrels. I don't own a 270 but loaded with a Nosler partition or accubond it's plenty to kill anything in North America.
I do own a 6.5 Prc it's currently the only magnum class chambering I still use. But it's not doing anything a 270win hasn't been doing for a 100yrs. Newer bullets and faster twist rates make it even more capable now.
If you're buying a new rifle with longer range targets in mind might as well go with the "latest and greatest".