I would be comfortable with either a .44 mag or a .45 colt loaded to "ruger" power levels. My preference would be a medium to heavy hard cast bullet with a blunt nose though I would not hesitate to use a heavy jacketed bullet either.
A medium weight SWC will often penetrate as well as a heavy more blunt bullet like an LBT design, they just don't do quite as much damage on the way by. My hunting .44 prefers the 300 grain LBT design, but I wouldn't hesitate to shoot an elk with my little carrying .44 with a 250 grain hard cast SWC. That penetrates 20+ inches in meat, too, it just doesn't leave quite as large a diameter hole getting there.
In .45, SWCs say 270 grains and up, or blunter designs 300 grains and up, should be fine.
So far as jacketed bullets, well, now that Nosler has discontinued the handgun partitions, my first choice is a Speer unicore plated flat point, 300 grains in either caliber. In .44 other things I'd happily use are the 265 grain, .444 marlin -designed flat point hornady and 270 grain speer flat point. I'd look at the Sierra flat point in either caliber. I would want to expansion/penetration test any of the 300 grain hollowpoints, I've only used them on deer and it's hard to learn much about expansion or penetration on a deer's head.
Anyways ... I'd love to have a .454 but I sure would not skip elk season if I "only"
had a .44 mag or stout .45 colt.
Tom