I'm assuming you are talking about cast bullets in sixguns, not single shots. A jacketed bullet is built to expand, & the newer one's do as advertised, they not only expand but the better one's penetrate much better than the old styles I grew up with in the 60's & 70's. I took a few deer back in those days with jacketed & they worked but weren't nearly as good as what we have today.
Mark Hampton is one of the top handgunners in the world & a great ambassador for our sport. There are very few out there that can match his experience. Ken O'Neill has also hunted all over the world & taken a lot of game that is bigger & badder than our elk or moose. I know Ken & he's not only a fine shot but but a lot of fun to be around, we've shared some good times together.
I've only taken one elk with jacketed slugs & it worked great, it was a Speer 270 gr. Gold Dot & the cow only needed one shot. The 5-6 deer taken a long time ago with the old style Speer 3/4 jacketed slugs also worked but for the most part was just shearing off the nose, which was pretty much soft lead.
I've taken many elk (10) & one bull moose, lion, bears, antelope, hogs & some African plains game with cast & never had a problem, I can't remember shooting one twice. Would they have died qucker if I had used a jacketed slug, probably, but I seldom have one travel more than 10-15 yds before going down, many went down at the shot. For the most part I'm a heart/lung shooter but many have been dropped with the shoulder shot. The part I like best with a quality cast slug is the penetration. I've never recovered one, whether its been elk, bears or moose, I know that slug is going to exit.
If a person is shooting a single shot handgun then a cast won't come close to the performance of a good jacketed slug. You need that big flat nose with cast or they will fail.
One time I was hog hunting with some friends (high fence) & although I wasn't actually hunting I was carrying a Browning Hi-Power 9mm & it was stoked with a little 120 gr cast truncated cone bullet. One of my buddies shot a nice size boar but hit it too far back & he ask me to finish it. The hog was down but not out, that little 120 gr cast slug went competely through the head & buried in the hard dirt behind it, a jacketed 9mm bullet wouldn't have came close to exiting on that big, hard head, it would have flattened out the size of a dime. Shooting it behind the ear would have done the job but I wanted to test the cast slug.
Dick