I'm on my second VT1 DI-EQ. I sold my first one because it was a hassle having its own power supply (they are 12v, centre positive supply - the opposite of standard 'Boss' style pedals), and I thought I could get the same sound with other pedals.
Turns out I couldn't. The mp3 and headphone sockets mean that I can practice at my kitchen table through headphones and still get a great bass sound.
Compared with the MXR unit the overdrive sound on the VT1 is massively superior (IMHO) - it'll do tiny amounts of breakup to full on fuzz if that's how you want to run it. The big difference though is that the MXR is 2 channel, so you can set a clean channel and a dirty channel, whereas the VT1 is single channel on/off unit.
You've also got a blend control on the MXR and not on the DHA, but to be honest, I've never missed it.
The MXR automatically adds a 'mid scoop' on the O/D channel if I remember correctly, making you sound great when you're playing on your own, but put that in a band and you'll just disappear in the mix. That's what I found anyway.
I never gig without it.