I had a BAII on my mid-70s Fender Precision. I recently replaced it with a Gotoh 203, since I want to get back to a more stock sound/appearance. The 203 is a bent plate bridge, kind of like the stock bridge, just a little heavier.
I've used the Gotoh 201 on a Squire 70s Vintage Modified J, and it's a good bridge. Buzzardsbass.com also sells what is essentially a Gotoh 201 for about half the cost. It's called the OEM Deluxe.
http://www.buzzardsbass.com/parts/bridges/econ.html The Gotoh 201 is about $40, and the buzzardsbass version is about $22). I've got the buzzardsbass bridge on an SX, and can tell no difference between it and the Gotoh 201. So if you don't want to spend a lot of money, I'd recommend either of those.
The BA II is a nice bridge, but I really can't tell any difference between it and the Gotoh 201 in terms of tone or sustain.