JMO from my 30+ years of elk hunting...

It sort of depends on what you are hunting and your hunting style, ie, trophy bull vs meat cow, dark timber vs long range, etc.

I have taken maybe them with bow, with 30-06 and with 300 WM. Obviously I like 308 caliber. I have seen good shots take nice little 5x5 bulls in dark timber using an open sighted 30-30 at maybe 50 yards.

One key is to use top quality bullets and know where to hit them. If you can discipline yourself to take only heart-lung shots at under 150 yards, then a 95-100 gr Nosler Partition in a .243 would probably do OK. But if you want to take a trophy if it appears with a raking shot if that is all that is presented, use nothing less than a 308 caliber and 180 gr top quality bullets, ie, Nosler Partition, Barnes, Trophy Bonded, etc.

1600-1800 foot lbs of energy at point of impact has been suggested by pros. That is a good suggestion.