On my J basses I’ve got a Schaller locking bridge, a couple BA II bridges, a Babicz, and a few Fender Pure Vintage bridges.
The Schaller and BA bridges came on their basses from Fender and the vintage bridges and Babicz were replacements for OE bent plate single string slot MIM bridges.
TBH, I can’t tell if any of these bridges make any difference in tone, but playability is different for each bridge. The Babicz by far offeres the most improvement over the bent plate, followed by the Schaller. The BA II bridges don’t work any better than the threaded saddle vintage bridges, but they are not worse, but the threaded saddle wins because it allows (limited) string spacing adjustment.
While they are all J basses they have different pickups, control setups, even an active bass in the mix so my take would would be a completely subjective personal opinion on tone/sustain characteristics associated with the different bridges.