I own a M625-9 in 45LC.
I don't hunt with a handgun, and I don't think I would want to. My hit probability is a factor of ten higher (at least) with a rifle, so its not something I would care to try.
So I don’t need to or want to shoot super hot loads.
The 45 LC is an excellent medium powered round. In the M625, you have a good balance of weight, power, and on target “thump”.
This is very non scientific, but a 255 L bullet traveling 850-900 fps hits my gong target with plenty of thump. 44 Magnums hit harder, but they also recoil more and weigh more.
I have been very pleased with the accuracy of my M625. In 1989 S&W started reaming the ball throat diameters to .452 instead of the older .455. This improved accuracy tremendously.
So, what do you want? If you want magnum performance I would recommend getting a magnum. If you want something that is portable, an excellent self defense gun, the M625 is an excellent choice.
I have N frames in both 44 Spl and 45LC. With my handloads there is little difference in terms of accuracy and gong target reaction out to 50 yards. The 44 Spl was made in 1986, the trigger has worn itself into perfection, and has the hammer mounted firing pin.
S&W also makes some fixed sight 44 Spls. I don’t think they are making any fixed sight 45 LC’s.
A fixed sight revolver is as simple as it gets.