Shoot em where it counts and the difference is academic.
Elk are big and tough, but they aren't bulletproof. This I know. Both choices will be fine. I used 150gr cup and core bullets in 30-06 for elk for years. Hit them good and they fall down. Of your choices I'd favor the '06 with 165gr partitions. What bullet you shooting in the 8mm?
"Once you quit hearing sir and ma'am, the rest is soon to follow." - Cormack McCarthy
"Feed me, or feed me to something. I just want to be part of the food chain." -Al Bundy