Here's where the dada fanboy in me comes out. Years ago, I custom ordered a single cut, Jerry Jones bass, red. Yup, I bought the same bass that Joie uses live. It was my main (and only) bass for eight years before I went back to long scale instruments.
I've owned both JJ and Danos, and there are big differences in the build quality/parts. I naturally relic'd that sucker for all those years, and it's still in great shape.
I like the JJ because it's unusual, and is light weight.
Now, shorties are a different story. I've found that my playing style changes quite a bit between short and long scale. When playing short, I tend to be a busier player, running lines all over the place. As a long scale player, I tend to keep it in check.
Would I buy another JJ? Probably not. They're cool for what they are, but you kind of gotta like what they are. I always had dreams of having a luthier build a body outta wood, and bolt the JJ neck to it. That being said, I've been meaning to dust mine off, and play her a bit.
On the plus side, you can get Dano's pretty cheap on the used market.
Getting back to dada.
If you're going to dada tone, Joie plays through an old Ampeg SVT. I think that's where most of his live tone comes from, plus he detunes all his strings down a whole step, and mostly plays with a pick. For some reason I have the impression that the JJ is just for playing live, and he doesn't record with it.