I don't like the Fender BBOT as I find it uncomfortable just where I rest my hand when playing. I have tried BadAss, Hipshot A style, Gotoh 201 and cheapo Gotoh-a-like. I wasn't particularly aware of increased sustain or improved tone, but then my ears aren't what they were. But all of them proved more comfortable when resting my hand on the bridge, so have stayed on.
I found the best quality by a country mile is the Hipshot A style, a remarkable piece of engineering that is adjustable in every dimension, including the 4th. Heavy, though, and expensive. BadAss was ok but, IMO, overpriced for what it does. Gotoh 201 is very good. Gotoh-a-like nearly as good and, for my purposes, probably the best value for money as it was only around £13 on eBay. Not as well engineered as the proper Gotoh but it does the job.