The 357 Magnum reigned as the most powerful factory loaded handgun cartridge for about 20 years (1935-1955). It's intended purpose was law enforcement. I'm sure it was also used for hunting to some degree. Like the Ruger Alaskan of today or a 4" S&W 500 Mag revolver, the priest was carrying the most powerful handgun of the day (357) in Alaska. The story is probably true.
Elmer Keith was probably most responsible for development of the 44 Magnum. But he was a man who used more gun than many feel necessary for hunting (not less). He hunted on horse back a lot and always had the six shooter handy. He took game with the 44 Special magnum, but it was probably more a case of opportunistic shooting than setting out to hunt say elk with the six gun. Development took 30 years for the most part.
The 44 Magnum was introduced in 1955 and it really was the most powerful production revolver caliber of its day. The 454 Casull didn't show up until the early 1970's and they were essentially custom made guns with a "wildcat caliber". North American Arms made some. The first Freedom Arms 454's that were factory produced showed up around 1983 even though the 454 was being experimented with in the late 1950's. So, the 44 Magnum gained the upper hand for about 25 years as the most powerful commercial handgun caliber.
Now we have an almost common place acceptance of these powerful calibers in handguns and people are taking them out specifically for use with dangerous game. I bet Dick Casull or Wayne Baker (Freedom Arms) didn't hunt grizzly without a rifle backup even though the pictures show one of the Freedom Arms revolvers posed with the shooter over the animal. Handgun hunting (for sporting purposes) only really started in the 1950's and is only today beginning to reach some acceptance with hunters.
Enter the 460 and 500 S&W calibers. Clearly the most powerful handgun calibers unless you consider a 45-70 a handgun caliber in the BFR or contenders.
The point of all this that you need to put the discussion of caliber in perspective of history. It is easy to say that the 500 makes the 44 common place in power. I doubt that many can spend a day at the range shooting 44's comfortably. The 44 magnum remains very powerful and with heavy solids is fairly practical backup for dangerous game, or a gun to carry camping or fishing where you might encounter one of these beasts in an unsocialable mood. It is a very effective caliber with a wide range of commercial loadings. (But I still prefer the 41 magnum.
)