I have been hunting with handguns since back in the mid to late 80's. There are plenty of revolver loads in calibers from 357 through as big as one can handle that will reliably put a medium sized deer on the ground if the shooter does their part. The "shooter" part of the equasion is the biggest pitfall though.
Me personally, I have shot several big hogs out past 100yds, and a couple of deer under 25 and one doe at 73 steps with my GP-100. I will tell you up front that it takes dedicated practice to hit reliably at distance. With my scoped 44 Redhawk off a rest, I shot many 1 - 1.5" groups at 100yds, and thought I was pretty fair. That was until I watched 5 of the Ruger team shooters come out to the 200yd range using the then new Super RH and do the same with open sights. Then again they were shooting upwards of 300 rounds a week as well, so as the adage goes, practice makes.....
One of the bigest issues with handguns is they usually have sights which do not allow one to draw a fine bead. Most are in the 1/8" thickness realm, are either black or bright orange, neither of which are really good for hunting, and most all of which block out a significant amount of the intended target. Once upon a time Ruger sold V-notch sight sets which fit both the GP-100's and the Redhawks. These had a very small brass bead on top of a very thin front blade making it real easy to get a fine bead on just where you wanted to hit, as well as not blocking out half or more of the game. These are what I used for many years. However like most have mentioned here, when your eyes go south, and your now depending on added magnification simply to see period, the "finer" things in life sometimes have to be adjusted to something a bit larger. Whats funny is I have come to realize, this doesn't just necessarily stop with sights...
I can still reliably hit a nice sized feral hog at 100yds with anything from my 357 to my 454. What I have found is that your bullet weight and profil are what will make that hit lethal if it is put whee it needs to be. In my 357's I will hunt with nothing under 160grs, in the 41, if using jacketed I use the 200gr Remington SJHP bullet over a decent dose of 296, and if using cast, I have now worked up a load using a 220gr WFN bullet over 2400 that has a ton of promise. In the 44, nothing yet but the 240gr Remington SJHP or the same weight XTP. Either of these shoot awesome and both hit with plenty of authority. In the 454 I only shoot the Lee 452300 RF that I cast myself over a charge of 296 or AA-9 either of which runs right in the 1550fps range. This particular load will slap a 200# feral hog right off it's feet at most any range I connect with one and I do not hesitate to reach out on them when I catch them in the open pasture. Granted I miss more often than not, but I just have this stupid stigma in my head that makes me hold over for the longer shots. Trust me when I say, that 454 doesn't NEED hold over till you get out plenty past 100yds.