I've got 2 highway one j basses with BA bridges on them, an MIM with a babicz bridge on it and an US Jazz plus bass with a machined Schaller bridge on it.
The BA's and Schaller were all original equipment on the basses they are on and all work well. That said, of these 4 basses I like the Babicz equipped one best of all, but only because of my kung fu death grip playing style and the fact that the strings on the Babicz feel (for lack of a better term) more planted than any other bass I own.
If you are looking to improve the sound, it's pretty much the consensus around here that there is not enough difference in tone or sustain to justify the cost of your typical aftermarket bridge. Some claim they get more sustain/richer tone, but they are in the minority. My personal opinion is it's an electric bass and I paid good money for an amp that handles my tone and sustain so I can adjust it to my liking no matter the bridge I'm using.
I'm also in the minority here about tangible benefits of an aftermarket bridge, but it is because of my choking grip playing style. When I get wound up I will drag strings out of position on any bridge that does not (by design) physically prevent me from doing so.
All that said, keep in mind it's your bass and you are the only one who has to be happy with it. The only reason you need for an aftermarket bridge is you want one. If you are looking for a different sound, (again) the consensus is pickups are the thing to look at changing to better achieve that goal.
"Strictly speaking, there is no certainty, there are only people who are certain." -anon-