I've been agonizing over the relative strengths and weaknesses of the BDDI and the VT bass for weeks, including far too many hours listening to youtube demos with my studio monitor headphones on. Plus, I've owned two SansAmp BDDI units in the past. Here's what I think.
The VT is going to give you a slightly warmer, richer retro rock sound. It's got mid control and it's got a defeat switch for the cab simulation. Basically, it sounds better and is more flexible.
The SansAmp is no slouch, either. It has great emulation of old retro tube rigs. The overdrive is good when used at low levels, but tends to not sound as good as the VT when you turn it up higher. It does not have a mid control, nor a cab simulation defeat, which means you'll always have that scooped mid sound with little way to get around it except to turn the effect down with the blend knob. Still, this pony does it's one trick with aplomb and it has a great DI plus a parallel out--really useful for both live and recording situations.
Either will work pretty well for what you're trying to achieve. The VT has warmer grit and more flexibility with regard to tone. The SansAmp does it's one retro amp sound very well and has some technical features that you may find really useful.
I guess it would be easier if I just told you which one I think you should get. Well, I can't do that. But I can tell you that I've owned two SansAmp BDDIs and I'm currently pining for a VT Bass pedal.
Good luck.
