Hi:
I've owned both. My normal rig is an Alembic F2B through a PLX2402 and Epi speakers. I got rid of the BDDI because my Sadowsky Standard 4 bass also cuts mids, and I was losing notes high up on the neck.
resuts: the para DI really brings the mids back up front, I like the way you can select your frequency and boost it as opposed to cutting both bass and treble on the BDDI to get mids. The drive control IMHO is better, I like the edge you get, although very similar to the BDDI. I have a Fulltone to get Jack Casady tone when the need arises.
problems: the para seems to really add a bit of compression, I lose fingernail to string noise and it bothers me. Also, I have to crank the treble up quite a bit to get my sound, if you are a thumper no biggie, but if you go for high end Entwistle type tone be prepared to crank up the treble.
Also, the volume/drive controls are very interactive, to get a clean sound you practically have to turn the drive off (and it is not 100% clean), but with some modification I like the final result with the para driver more so it's a keeper.
Still fighting the compression issue, tho . . . . . . .
Phil Anderson
Tucson, AZ