I had a chance to try out several DI's in the meantime and wanted to share my experiences with you...
(all DI's tested with a passive P-Bass in the studio with a Toft ATB24 Analog Mixer and on a neutral sounding Yamaha PA).
Pls note: these are just my subjective impressions
BDDI
Well known and discussed a lot...
With the Sansamp emulation de-activated the box is a simple DI without much coloration. Sounded a bit whooly / soft to me (in comparison to all other DI's).
Much better sound with the Sansamp emulation of course. Still you have to dig the sound (best to play with the bland knob!). Nevertheless I was a bit disappointed in the power & sound of the DI out (I played a ParaDriver for several years) in the studio.
Radial JDI
Passive bass with the passive JDI. I was excited to hear this combination.
In comparison to the active DI's you definetely notice a loss in level and frequencies. The JDI does load the passive pickups as far as I understood, which causes a difference in sound.
But I have to say that the JDI wins in terms of "sound" (although this is some sort of "coloration" in the end). As s.o. stated above P-Bass + JDI = great match (unfortunately I had no comparison with another bass). The P sounded really smooth and a bit "woody" in the mids. The highs were rolled off (compared to the active DI's), but didn't sound lifeless or muddy. What I didn't like was the sound of the bass frequencies. They were to much highlighted. Nice for some people but not for me. Too bassy in the end.
If you like a classic vintage orientated sound (which I also like sometimes) you may prefer the passive JDI with a P (will for sure sound different with an active bass). When it comes to preamps in front of the signal chain we are talking about a whole different sound. I didn't like the JDI in combination with some preamps (unfortunately I like to play with them so the JDI was not the best choice for me in the end).
Countryman 85 / 10
I ordered both of these units because I was curious if you would hear a major difference in terms of sound / level etc.
The Type 10 is supposed to be some sort of devolopment of the trusted Type 85 I guess. According to the data sheet you'll get less distortion etc. bla.
When I compared the two DI's I heard a difference in the shaping of the sound. It's difficult to say, but the Type 10 sounded a bit more hifi than the Type 85. Noticeably more lows, a bit more "high end highs" and overall a bit more output.
In the end I liked the Type 85 far more! It is still very "active" sounding (compared to the JDI for example) but there is something going on that makes it sound really tight. Bass frequencies are not as strong as the Type 10 (which I prefer) and the highs are getting smoothed out a bit (not as much hifi-sounding). Don't get me wrong, it is still very neutral sounding, but with a slight touch of tube flavour (compared to the Type 10). I guess this is the overload-behavior of the class A FET amplifier in the Type 85. Behaves just like a compressor in some way I think...
Paired with preamps the Type 85 still sounded very good and I liked the overall sound a lot (better than with the JDI).
SPL Gainstation
Actually this one was sitting on the desk of the studio. I tried it out and really liked it so far. But hey - I would never take it out on a filthy stage for that price!

But I get the whole tube-preamp-REDDI-TheBrick-thing...
In the end a DI should provide a good clean signal to the console / PA.
I expected that you would only hear major (sound) differences in the studio. On stage this is is a whole different story. Nevertheless you can also hear the differences in a loud live environment. For example the Type 10 sounded extremely clear and bassy (best for modern tones and 5-6 strings I would suppose) where the JDI was a bit more shy and colored due to the passive circuit.
I guess it all depends what you want to achieve with your whole setup...