Are they worth it? For some folks they are, for some they ain't. I used to manage a guitar store (1977-1988) and I've owned some basses with BA-II's on them. For me they are not worth it. I LIKE the way a stock Fender vintage style bridge works and how it sounds. I don't want more sustain, I've never owned a Fender with falling saddles that I couldn't fix, and so there's no reason to change them.
The deal? The original Badass was designed to help with specific problems on GIBSON basses. Those basse's stock saddles would be nylon, lots of moving parts that weren't particularlly stable, and the didn't offer much range of motion. So the original BA was made to give those Gibson's a more stable bridge with enough range of adjustmetn to get it into tune and the action where it needs to be.
In the '70s people playing new Fenders that weren't as good as old ones were trying anything to make them sound better. Someone started putting Badass bridges on Fenders, but the original ones were very tall (remember, they were designed to overcome shortcomings of the Gibson bass bridges) so you had to route out wood to set the BA into a Fender body. There was enough of that happenng that Leo Quann started making the BA II specifically for Fenders. It's just a BA with a smaller base plate that allows it to sit on top of a Fender bass body without routing. If you have a Fender and you want to try a BA, make sure you get a BA-II.
You say you've got an American Standard however. That bass already has a bridge with a lot of the useful features of a BA. It's got grooves to keep the saddles from sliding side-to-side, it's got a bit heavier base-plate, and heavier saddles than a vintage style Fender bridge. I'm not sure what a BA brings to the table for that bass.
jte