For factory loads, I have had good experiences with the 44mag Hornady 225grn FTX Leverevolution, 240grn XTP, and 300grn XTP loads. I killed a dozen or so deer back in the late 90's and early 00's with simple Winchester white box 240grn SJSP's, never had a complaint.
If you're rolling your own, I've become a big fan of the 300grn XTP, as well as the 270grn Speer Deep Curl. I rolled a LOT of 225grn Leverevolution FTX's for a couple years, still a big fan, I've just been playing with heavier jacketed bullets of late, favoring the momentum of 300grn pills. (I still haven't convinced myself to go back to lead pills).
A bit of a reality check:
the 44mag will cleanly kill a deer at ranges beyond 100yrds, even from a revolver. The shooter's ability to deliver the shot is really the major limiting factor for 'effective range' in a 44mag revolver. A .357mag might find itself wanting for power beyond 50-75yrds or so, but the 44mag will typically have more energy left at 100yrds than the 357mag had at the muzzle - more than enough to put deer in the dirt with ease.
BUT...
Are you actually capable of delivering 4-6" groups consistently at 100yrds with a revolver in field shooting conditions? Probably not.
Street Doctor rightfully mentioned the expansion velocity specs for bullets, but in general, even big fat 300grn 44mag rounds will be over 1000fps at 100yrds, so again, plenty of velocity to promote reliable and efficient expansion.
I can't shoot nearly as well as I could a decade ago, but I still hang around. Making 50yrd shots on deer with my hunting revolvers isn't off of my table, but I know my 100yrd revolver deer hunting days are behind me.
I've been hauling this one afield for over 15yrs, taken dozens of meat doe, quite a few coyotes with it, and a handful of piggies.
Here's a couple recovered 225grn Hornady FTX Leverevolution slugs, plucked from the berm behind my targets in the yard. These are a bit more cleanly/evenly expanded and retained weight a bit better than what I expect from the same bullet on live game, but the expanded diameter is about the same:
If I don't cut the barrel down before deer season opens this year, I might take this 7.5" Vaquero 44mag out after deer (the nose job on the 5.5" Bisley has already started, and the lipo on its hind end is done already too!):
I took this 5.5" Super Redhawk after hogs back in June. Granted, it's a 454C, not a 44mag, but the second day I just used some hot loaded 45colt instead of the punishing 454's that were about on par with factory 44mag specs:
Again, without question,
your accuracy FROM FIELD SHOOTING POSITIONS will dictate your effective range. I've seldom met non-competitive handgunners that could deliver 50-100yrd huntable accuracy from a revolver, so ultimately, the retained energy at range is moot.