I think if one action type was very superior to others, then the rest would have faded into history. The anson and deeley boxlock is probably inferior to a lot of sidelock actions, but yet it is a popular, strong, probably easier/cheaper to produce and adequate for shotgun pressures.

The Rigby/Bissell rising bite action is extremely good, being strong enough for double rifles as well as shotgun usage, but fell from favour as it was very expensive to make.