well this was fun to read. I've only gotten 2 elk over the past 20+ years, we in AZ don't get drawn every year and I don't put in every year, but when I do, I almost always have friends and relatives on the same hunt. So thinking over the years hunting with my brother, son, nephews and hunting partners, we've only gotten cow elk. Every one of these, except one, I helped gut & load into my truck, so its fairly firsthand experience.

.270Win - M70 push feed - 150gr Kodiak handload
.300 Win Mag -M70 CRF - 180 gr Fed factory
.30-06 - Butcherized 1903 - 180 gr Fed factory
.300 Rem Ultra Mag - M700 - don't remember the load my friend used, probably factory.
.300 Rem SAUM - M700 - 180 gr Hornady BTSP handloads
.257 Roberts - M700 - 115 gr partition handload
.270Win - M70 CRF - 150 partition handload
.270Win - No1A - 150 partition handload

so I guess around my campfire the .270 Win wins the popularity contest, unless we count.30 cal of all chamberings.

Poole