I still swear that there is not one single component that lends itself to be the one consistent thing that causes increased sustain, lower frequency transfer, etc. I say this just from MY experience, but it's been proven to my ears a few times. If a bass is a dud, and the sum of the parts just doesn't create something stellar, adding a high-mass bridge isn't going to magically bring it to life.
I have a Fender American Standard with the Fender high-mass bridge. I also have a G&L with the massive high-mass bridge with the route that seats it into the body and the screw that locks all the saddle together and supposedly makes it most efficient, solid, etc. I had an older, 10lb '76 Fender Precision bass that I got with a Badass II bridge that I later switched to the original, cheap, bent saddle bridge with the threaded saddles. I also have a Classic 50's P with the stock vintage style bridge and a '96 MIM Standard with a vintage style Fender bridge.
My conclusions...it comes down to a combination of EVEY component and how they all interact and work with each other. It's kind of a roll of the dice and hope for the best. Wood is organic and you can't really predict how it with the body and neck will interact together, resonate, what frequencies it will attenuate or accentuate, and how those materials work with each other, etc.
With that all said, I still prefer the thin, cheap, bent, vintage-style, regular old boring Fender vintage-style bridge. Every bass I've owned that has had or has any sort of high-mass style bridge seems to suck some of the inherent, individual characteristic tone from bass and just makes it sound more "generic". It may or may not increase sustain, but overall I feel like they kill the inherent tone of the instrument, or dulls/attenuates it like a buffer.
On the '76 P with the Badass bridge it sounded like any other P bass, nothing spectacular, not bad, but nothing to write home about. When I put the cheap, original bent stock Fender bridge back on the basses woody, resonant tone came back, while still retaining the same amount of sustain and thump, but had better tone (subjective, of course). My Classic 50's P is my most resonant, fullest and probably best sounding bass I own, and the '96 MIM is a very close second. these two basses vibrate in your hands when you play any string like it's alive, and both have sustain for days, and both of these basses just have the crappy, stock Fender vintage style bridge with threaded saddles, and both basses weigh 8.4 and 8.6lbs. respectively.
I'm NOT convinced high mass bridges do anything other than maybe empty your pockets of cash a little quicker. The way they alter the tone just seems to suck some of the true sound from the instrument, and I don't think they do anything for sustain, and for the sound I'm going for, and seem to rob the bass of some of the natural, woodier sounds.