I would limit my range to 50 yds with the 357 and 100 yds with the 44 mag as long as you can consistantly hit what you are aiming at. I believe it is a matter or ethics and confidence based on range experience. Personally, I feel the 357 a little light for whitetails and Kansas whitetails tend to be fairly large. The other variable is that you can hit pretty well from a bench at the range, but are not nearly as good with an off hand hold. Practice this way. I carry a shooting stick for this purpose which slows things down considerably but I feel more confident with my shot placement. Still hunting, I try to always position my self near a tree for a rest also. Sometimes it is impossible though and you just do the best you can.
The business about an immediate knock down versus following a blood trail is one that has always concerned me with handgun hunting for whitetails. Most prefer a solid heavy bullet versus a hollow point design in order to get maximum penetration and go through the animal resulting in a two holes for more blood to leak out. With the larger calibers (>357), I feel this is less important as far as hollow points go as they should penetrate. I also would think in terms of a fast followup shot if they don't go down immediately (ie don't wait to advance the cylinder to the next round with the thought "I had a solid hit. He has to go down". I'm new to handgun hunting and have struggled with these issues.
For me, 50 yards is about the limit hand held and 75 yards is about my limit off a rest. You just have to make your decisions as you go along. Would I take an 80 yd shot with a large caliber handgun (in my case 480) and a rest, probably.
