Were a quantum leap forward in reloading speed when they first appeared. MUCH faster than the usual single action (colt style) system.
Accuracy? In principle, they should not be as accurate as "solid" frame revolvers, but, in practice there isn't any significant difference in average hands at normal pistol ranges.
Some models of top break revolvers were target guns and were quite popular for many years.
What killed the top break revolver as a serious use gun? A number of things, including cost and complexity, but mostly it was the in ability to use a powerful cartridge. There are no top breaks in magnum calibers, and even the original .45 Colt loading was not useable in the original S&W N0.3/Schoefield guns, as the cylinder & frame were too short to take the length of the round.
Modern "reproductions" of the S&W can be had in .45 Colt, but loads must be suited to the gun, no magnum or "Ruger only" level loads can safely be used.
Even the big Webley Mk VI is strength limited. Many (most?) of these gun were converted from .455 Webley to .45ACP during the 50s, when original ammo was scarce. But the .45ACP in ball load is essentially a proof load for the Webley, and should not be used. If you have one of these converted guns (using full, 1/2, or 1/3 moon clips), use the ACP brass and load "light" (compared to .45acp) to match the .455 pressures.
There are tons of .32 and .38 S&W top breaks out there, mostly very cheap guns, cheaply made, and cheap when new. The best of them, in good condition is a decent gun, providing one doesn't expect more from it than it is. But there were a great many that are (and never were) the best.
All else being equal (and it almost never is) bigger bullets tend to work better.