I don't know if it still applies in competition, but at one time if the bullet hole cut the scoring ring , the higher score was awarded. This makes the larger holes of the big bore a better choice from a target shooting point of view. The report of the .357 is very sharp, and if you happen to fire one without proper hearing protection, chances are you won't do it twice.
As an ATC gun the .44 is leaps and bounds ahead of the .357, but that only counts if you can shoot it. As a handloader, you can load a .44 to your comfort level, but for protection against large predators, it is at it's best with a 300 gr hard cast bullet at 1200 fps. A 180 gr hard cast flat nosed bullet that hits the mark from a .357 is better than a fatter bullet 100 grs heavier that misses.
I owned and shot a half dozen .357's before I got my first .44, and once I got a .44 I wondered what all the fuss was about. It will do anything the .357 will do and do it better, however I would suggest the .357 as a first gun.