I'm not terribly familiar with Jeff Berlin's work (yet), but I just heard the song "Joe Frazier" from Bill Buford's band, and man, I love that tone. How can I get that tone, besides just being super awesome? Is that mainly just bridge pickup and playing close to the bridge? I've tried that before with my bass, and gets closer to this sound, but when I do it it's nowhere near as fat and nasty.
There is a old VHS Berlin instructional video where he talks about his gear that is probably closer to the time-frame of those Bruford albums. I don't know if the clips ever made it to you-tube yet.