The first is when something happens unexpected and you are left to dance with the girl you came with. The other is when you can choose which handgun you feel most comfortable using weak handed. In both situations the shooting part is not that different and with just a little practice most any of my handguns will perform at least as well as with my strong hand. Reloading though can be a major issue. Racking a slide is REALLY pistol specific and quite a few of my pistols one hand racking is nearly impossible. Rounded curves on the slides and sloped sights add to the difficulties and things like magazines that do not drop free (HPs) can add complexity even when most controls are ambidextrous. When I carry one of them I always try to have at least one fall back option.
In revolvers, the Smith push to release the cylinder is easier to handle one handed then the Colt pull to release and the rounded Colt cylinder release just makes things even harder. The simply angled release on the early Colt revolvers like my New Service made in 1919 is easier than even the Smiths.
The two easiest revolvers to use weak handed are my Dan Wesson 15-2 and an old Webley Mark IV. The cylinder release on the Dan Wesson is in front of the cylinder and you pull a lever down while pushing from the reverse side to swing the cylinder out. From that hand forward of the cylinder it is even possible to reach back and push in the plunger to eject all the cartridges. On the old Webley the release lever is big and wide so even weak handed you can break the gun and pushing the barrel against body or other object ejects all the cartridges and sets up a reload. In all my revolver practice I try to include loading the cylinder two cartridges at a time as well as various speedloaders.