Hi,
I have used the VAP for a couple of weeks now on gigs, rehearsals and a recording session. It's an easy to use, great sounding and versatile preamp. Unfortunately I'm not doubling with it, nor am I using piezo pickups so my situation is probably a bit different from yours. Nevertheless (I think) that the VAP does do something similar to those other excellent tube DIs that you mention as it contains a proper transformer and runs higher voltages through the tube rather than starving it with 18v or something similar.
When powering an Ischell C3 contact microphone, introducing the tube circuit really helps to smooth out the throaty edge from the amplified arco tone. Playing pizz with the same contact mic, the tube circuit seems to bring out more of the finger details and the upper end of the spectrum. In general, I've found the direct sound of the VAP to be much more pleasing and even realistic than it was possible to get with the original EDB-2. Also, the specific effect of the tube circuit on the sound seems to really depend on the character of the source and the amount of preamp gain that hits the tube circuit. Add to this, the possibilities of tube-swapping (which I have done with mine). If pushed hard, it does get that saggy thing starting to happen (possibly a cool sound with a p-bass) and there is a bit of noise introduced with the tube circuit. However, I can't say if the noise floor is more or less than with a fine tube DI like a radial firefly or a U5.
The form factor of the VAP is pretty awesome as well. It's still lightweight like the other EDB-2 models but with slightly bigger knobs which make it easier to adjust while playing. I keep it on the floor beside me.