There's really no reason to own a .41, period.
The .44 mag does everything a .41 does and more. You can create light loads or heavy loads, and the .44 works better against large animals. It may not be that much better, but it does add the extra oooomph that the .41 doesn't have.
The .41 was designed mostly for law enforcement personnel who wanted to add substantial power to assist them in their jobs. In short, they wanted to add some power to the .357 magnum round. Did this happen, and was it needed? In my view, yes, it added power to the .357 magnum round, and no, it wasn't needed.
If the officer used loads that were more powerful than the .357, then those rounds would be too powerful for LEOs to use. Data collected over the past three decades show that the .357 magnum with 125gr JHPs to be the ultimate revolver manstopping loads. More power is not only not needed, but not wanted. Any .41 round would either have less manstopping power, or would encroach on the .44 magnum power.
Bottom line: The .357 is the ultimate revolver manstopper, bar none. Not even the .41 can beat it as the bullets generally stay in the body of the person being shot. In other words, to beat the .357, .41 loads would have to approach the .44 magnum's in power, and then there would be no reason for a .41 Also, any energy expended when the .41 (or .44) bullets passed through a human body would be wasted. Thus, the case could be made that the .357 125gr JHP could beat any .41/.44 for law enforcement purposes. And that any .41 load for big game would have to virtually duplicate the power/loads of the .44. So with that in mind, the .41 doesn't match the .357 because of penetration problems and doesn't do anything for the .44 mag, being rendered superfluous by both calibers.
Cases for the .41 also are expensive and difficult to find!