I've shot quiet a few whitetail dear with the 44 Mag. in a pistol. Like most folks I started out with a 240 gr. bullet, either jacketed or hard cast. They will all kill deer, but they don't have much "knockdown" power. They shoot holes through deer but don't have any shock power unless you hit a bone. The deer will run off like he's shot with an arrow. I once had to shoot a 4 point buck 3 times through the heart/lung area before he fell over. You could cover all three holes with you hand. He was just so interested in chasing a hot doe, he didn't know he had been shot. The bullets were 240 gr. Jacketed Hollow Points. I dug one of the bullets out of the ground and it had not expanded. These were loaded hot with a max load of WW296 powder. So I started shooting 180 gr. hollow points. The extra 300 fps, from 1400 to 1700 fps really made a difference. I've never looked back. Unless you're trying to stop a charging grizzly, you don't need a heavy, deep penetrating bullet.
If I want to shoot long distance with a handgun, I've got several high power pistols that I can use.
But if I'm using a wheelgun, I'm carrying my 6" S&W Mod. 29 loaded with Sierra 180 gr. Jacketed Hollow Cavity bullets.
Just my two cents worth after handgun hunting for 50+ years.