If I was forced to keep only one, it would have to be the BDDI because it's so versatile, although I probably use the VT bass pedal more often. The BDDI has a better sounding range of clean to distortion to my ears, but I think the VT is inherently warmer. While not perfect, it does a respectable job of providing a good "tubey" sound.
For the record, besides the above 2 boxes, I've owned the Leeds, Oxford, Liverpool, and VTDI Deluxe. I reluctantly sold them off because I can't justify having so many pieces of gear that are essentially redundant.
That said, I'm actively looking to get another Leeds pedal because it really is that good at nailing the Entwistle sound that I love so much. An added bonus is I found it to be excellent on guitar. I dabble at playing rhythm guitar and the Leeds pedal comes fairly close to a vintage David Gilmour tone.
I've been itching to try the YYZ pedal.