A lot of people confuse loose-saddle, high mass bridges with lockdown bridges like the Babicz or the old Gotoh's. Lockdown bridges can be made of lighter materials (the Gotoh is made of pot metal), and seem designed to connect the string more firmly to the body resonance, rather than isolating it like a Badass.
Either way, the differences are audible to me, but different doesn't necessarily mean better. Given the magnitude of the acoustic differences between supposedly identical Fenders, IMO the difference between bridges is just a seasoning, like choosing toppings for a Sundae.
I have an Ibanez ATK, which takes the "high mass" concept to its logical conclusion- the finish encases the body in a thick, brittle plastic staightjacket, and the bridge is massive. There are two grooves to keep the saddles from sliding side to side, but they're still loose from the backplate, like a Fender. The body is pretty much isolated from tone production, so it's all down to strings and electronics.
Somewhere in the middle, I had an AV '62 P-bass a while ago, with a light nitro finish over a fairly light alder body and the vintage "threaded saddle" bridge. The saddles were only coupled to the body mass by string tension, but there wasn't a ton of metal in the way.
At the far extreme from the ATK, the 5-string in my sig is a heavy neck-thru singlecut with an oil finish, and a light pot-metal Gotoh lockdown bridge. The wood-to-metal ratio is very high, and there's pretty much zero interference between the wood and the strings.
I like all three basses. The ATK sounds very "active", and the sustain is good but not great. Still, it's got an interesting range of tones, and it's great for fast, burpy 16th note lines. The Fender had about the same amount of sustain (and similar dead spots!), but with a classic passive P-bass tone, very woody and articulate. Meanwhile, the heavy neck-thru has a more woody character than the ATK (even though it's loaded with active EMG's), but not as much as the Fender. The biggest difference, is that it's so lively and has so much sustain, that it's hard to choke it back for staccato stuff. Great for legato lines, but it stinks for the burpy stuff where the ATK and Fender excel.
Back in Fenderland, a bridge change might have moved the AV '62 a tad in one direction or the other, but it certainly wouldn't have made it sound like the ATK, or my "Rolfodera"...