I had the L-bracket mounting system a long time ago and the biggest downside to that system is that if your triggers are too tall, or your flash itself is too tall (or more likely the combination of the two), your flash head won't be centered in the opening, or will only be partially in the opening. I eventually cannibalized the L bracket to mount to a chinatown special beauty dish, but it wasn't very suitable for the job.
The S-type mount fixes the flash head position and allows the speedlight body (and any attached triggers) to fall where they will. I'd imagine this might put a bit of additional stress on the flash head since the hinge is designed to support the flash head, not the entire flash body (plus trigger). Either way, I'd go with the S-type mount if I were to choose between the two.