The .41 magnum can everything the .357 magnum AND .44 magnum can do.
I know the .41 Mag has a very loyal fanbase, but I think that statement is a bit of a stretch. I've had all three, and for me, the .41 is the least useful.
The .41 Magnum is a fine cartridge, but it isn't the .44, nor the .357 in a lot of ways.
It is a fine example of US gunmaker's stupidity. Several of the nation's top gun writers and others with LEO experience had reached a general consensus about what would be the best gun for police use. They felt that a .40/.41 caliber DA revolver, of medium size, firing a 200-ish grain bullet at 900-1000fps would be the best blend of size, power, and "shoot-abilty" for police use. They asked the major gunmakers for that. The gunmakers listened, but didn't hear...
What we got was the .41 Rem Mag, and the S&W M57 (M58 fixed sight for service use). Remington offered two loads, a 210 JHP/JSP at .44 Mag velocities, and a 210 LSWC at the lower velocity asked for.
The gun was bigger and heavier than what was really wanted, being an N frame, but might have been accepted, save for what Remington did with the ammo. And that was focus early production on the magnum ammo, not the law enforcement load.
Several major police agencies tested the .41 Mag, but at the time, the only ammo common was the magnum load, and that what they rested it with. Surprise, surprise, it was found unsuitable. The fact that Remington later made police ammo available was simply, too late. The .41 Mag as a police round was doomed. Bureaucrats (including police ones) simply almost never go back on their decisions, once formed.
interestingly enough the specs the writers felt would be best for police did turn up in a cartridge, decades later, and in an auto pistol, the .40 S&W.
TO me, the .41 Mag only makes "sense" in a gun like the Ruger Blackhawk, because it is a bit lighter than the Super Blackhawk, despite being about the same size. DA .41mags are all on the big .44 frames, and to my mind, if you are going to use a gun that size, going with a round that is 15% less (on paper) makes little sense. Also, I've never been able to notice the 15% reduction in recoil. Both of them feel about the same to me.