Howdy
I shoot Top Breaks in Cowboy Action all the time. I also shoot modern revolvers all the time.
There really is no advantage to how fast a Top Break ejects cartridges over a modern revolver. With practice, you hold the modern revolver in your left hand, pop the cylinder open with your right, and then with your left thumb you pop back the ejector rod to dump all the cartridges out in one quick stroke. With practice this can be done just as fast as dumping the empties from a Top Break. After that, loading either revolver is pretty much the same. In both cases the rear of the cylinder is completely exposed and you load in fresh cartridges. Speed loaders will help enormously with a modern side swing revolver.
The advantage of the Top Break in the 19th Century was it was much, much faster to reload than a conventional Colt. With the Colt, you had to put the hammer at half cock, and use the ejector rod to pop out the empties one at a time as you rotated the cylinder. Then you had to reload one chamber at a time as you rotated the cylinder. A Top Break was much faster than that, but the advantage pretty much went away when side swing revolvers came along. It just takes practice to empty and reload a modern side swing revolver quickly, it is no big deal.
Then there is the fact that other than the Big Number Threes, the largest caliber available for a medium frame Top Break was 38 S&W, not 38 Special. That modern J frame is going to be both stronger and more powerful than any Top Break of the same size.
Compare the lengths of these two Top Break 38 S&W cylinders to the length of the cylinder of the modern J frame Model 36. That is a good indicator of how much longer and more powerful the 38 Special is to the 38 S&W. Not to mention that 38 Special ammo is much, much more readily available.
By the way, it takes practice to reload a Top Break efficiently too.
P.S. I don't carry a firearm, but if I did, it would be a modern side swing revolver, not a Top Break.
P.P.S. Did I mention that S&W has not made a Top Break revolver since about 1940? Most of them were made long before that. The two pictured are antiques, made before 1899. Besides the fact that the modern design is stronger, modern heat treated steel is also much stronger.