I've shot my last 4 firearm whitetails with either a .357 or .44 rifle. Most of my deer are taken during archery season. All were with handloaded XTP bullets over a max charge of H110. I shot 3 with a .357 (Ruger 77/357 and Marlin 1894 CSBL) and 1 with a .44 (Marlin 1894). These were all meat harvest deer on a special hunt we do every couple of years. All the deer went down fast (within 20 yards) except 1 doe with the 357 which was running in the rain at about 80 yards and I only nicked the windpipe on during a snap shot, definitely my fault all the way. I found her bedded about 50 yards away that night and finished her off.
My last deer was with a .357 mag out the 16" 1894 CSBL. I was shooting downhill at 50 yards (about at a 45° angle) and wasn't a great shot through the brush. I hit the neck but not the spine yet the deer ran less than 15 yards. This is a fun handy little gun. I carried it for a week this year and really enjoyed it.
The first deer I shot with a PCC was a decent 6-point with the Ruger 77/357. No picture unfortunately. Shot in the high chest and the deer dropped in its tracks. I actually couldn't find the deer at first because I assumed it ran and I was too excited to see it go so I was busy looking for blood in the direction it was faced instead of walking up to where I shot it...
The .44 I used to shoot a buck coming into a grunt call. I shot him head-on at 10 yards, the bullet travelled the whole length of his body and ended up in his rump. Perfect mushroom, blew the hear apart.
My last deer and my Marlin .357:
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I was able to (poorly) record this shot:
https://i.imgur.com/FADo04V.mp4
My ruger .357 (took 2 deer with this gun):
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My Marlin .44:
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Bottom line: there is no disavantage to going with the 44 Magnum that I can see. It certainly gives you more power and the recoil is nothing worse than most all rifle cartridges. If you can shoot a 20 gauge you can shoot a 44 rifle. The 357 is just more interesting to me in a rifle for some odd reason. I truly don't know why. Originally I bought my first 357 rifle to pair with my Ruger SP101 and while they both do shoot the same load I never once even came close to having to use ammo from one to feed the other. My handloaded 357 rounds do 1746 FPS for 158gr XTP's and while this isn't extreme, it is certainly a significantly different round than when fired from a handgun. It is a true deer round and my 2 imperfect shots with recovered deer prove to me you don't have to heart-shoot a deer with a 357 rifle to successfully harvest a deer. I'd love to say I make perfect shots all the time but the still hunting I do with a rifle is always surprising and interesting and I don't think I've ever made a textbook shot even though I am a great shot at the range. Don't hunt with marginal cartridges and 357 is certainly not one of them.