Never hunted elk, but have shot eland ~2,000 lbs at just over 300 yards with a .338 (250 grain Woodleigh) as well as a leopard and other PG (225 Partition) and it worked well. On other hunts, shot lots of PG including waterbuck, zebra, kudu, etceteras with a .300 Win at various ranges (200 grain Swift A Frame) and it worked well, too. Took the .300 Win to Argentina and killed a large red stag decisively, same 200 grain A-Frame and it dropped at the shot. My buddy on the same hunt killed his red stag with a .338 (225 grain TSX). It was no deader than the one I killed with my .300.
If you are recoil sensitive, I took a .30/06 loaded with Barnes 168 TSX to Africa in 2018 on a cull hunt and was impressed with how well it killed various species, including waterbuck.
My conclusion is that careful bullet selection and shot placement are the critical factors, not bullet diameter. Pick the rifle and cartridge that you shoot the best.
