Sure I'll bite. There are two main cases where it could matter:
1) With a passive bass and no pedals or other buffers between the bass and the DI, a passive DI can load down the signal, reducing highs, and in some extreme cases weakening the signal overall. If you want a dark vintage sound, this may be fine.
2) With an active bass or with effects or some other buffer/boost between the bass and the DI, some 9V active DI boxes may distort on your signal peaks. To avoid this, you can use an active DI that runs on 18V or higher.
Based on those two cases, some people set a rule of thumb to use an active DI with a passive bass, and a passive DI with an active bass. But of course that's just a simplification and generalization; there will be lots of instances where passive works great with passive, and active works great with active. It depends on the specific gear at hand.
Thanks for that - pretty much what I've gleaned from my (limited) research.