I have used various cup and core bullet as well as "premium" bullets. If I were to give an overview it would be simply this: The smaller and/or less powerful the round the more help a Premium bullet can be. My definition of "premium" is about weight retention not just accuracy. Accuracy is never a bad thing, but for elk I rank accuracy as less important then good terminal performance (expansion with good weight retention)
But any bullet that can break bone and hold together is ok for elk. I have seen many and used some myself that were not so good but others were excellent.
Cup and core bullets I have killed them with:
150 grain Remington RN 270s (excellent) 150 grain Speer Hot Core 7MM (very poor) 175 grain 7MM, Hornady. (very good) 150 and 180 grain 30 cal Winchester Power Points from a 300 Savage, 308s and 30-06 (good and very good) 220 grain RN Hornadys (Very good) 220 grain Sierra RN. (very good or excellent)) 225 grain Hornady Spire Point 338s, (Poor for elk. Complete break ups) 170 grain 8MM Hornady SSTs, (poor for elk.) 200 grian Flat Nose 348 on a moose, not an elk, but it held together and did well. One kill only, so not a real good test, but I'll add it anyway. 270 grain Hornady Spire point 375s ( comes apart some, but gave me exist despite the metal flakes in the wound) 270 grain Hornady RN 375s, (very good) 270 grain Winchester Power Points (Excellent. In fact about the best 375 I ever used, and equal to the Premiums) Winchester 300 grain Sliver Tip 375s (some metal frags in the wounds, but give exits, so I can't complain) 300 grain Sierra BT. (Gave exits but I found the cores inside the ribs, one elk and one moose. Same on both kills. So this one could be called both poor and good. Poor because it came apart but good because about any 300 grain bullet from a 375H&H is deadly just owning to it's size and weight) 416 400 grain Hornady SP. (Works well but didn't seem to expand much. Smaller exit then I expected, but it killed the bull fine)
In addition to those above I have killed elk with the following "premium" bullets. 270s 150 and 160 Grain Nosler Partitions (Excellent) 7MM 160 and 175 Gr Nosler Partitions (Excellent) 7MM 150 grain Barnes X (Excellent) 30 caliber 165, 180 and 200 grain Nosler Partitions. (Excellent) 30 cal Barnes GMX 165 (Excellent) 180 grain Speer 30 cal Grand Slam. (Gave exists but some fragments in the wounds) 8MM 200 grain Nosler Partition. (Excellent) 338 210 grain and 250 grain Nosler Partitions (Very good and Excellent) 285 grain Speer Grand Slam 375. Did ok, but on elk it's basically like a solid giving me exits of about nickel size) 375 300 grain Nosler Partition. (Excellent)
In every case, the above listed "premium" bullets did all I could ask of them. I can't say they did a lot better then some of the best cup and cores, but never did I have a single failure.
Then there are those killed with cast bullets from four 44 magnum handguns, a 454 Casull, and also two 45-70 rifles and round balls from both 58 cal and 62 cal muzzleloaders. All my cast bullets and balls did the job perfectly.
By far the most information I have gathered from over 50+ years of elk hunts is from guiding, packing and butchering elk other then those I killed myself . In the last 1/2 century I have not only killed my own elk, but also helped in various capacities with a LOT more dead elk then I have personally killed. If I were to make a realistic guess I would say my number is around 90, and the ones that I have helped with are probably 6-7 times that many. I have seen them killed with guns from 243s to 50BMG. With handguns from 41 mag to 500 S&W and also with about 25 different arrows and broadheads. So if I am asked if you "need a premium bullet" in many cases I say NO!. But in all cases I would also say it won't hurt you to use one either.
