The 78 Distortion, though not as versatile as the DD, is more specific, and fantastic value for money. The Boss DS-1 is buffered, whereas the 78 is true bypass, as a result the DS-1 will colour your tone. This maybe more of a decider for you as a Bass player, this will will be more noticeable. The clip below gives a quick demo...hope this helps.Can't go wrong with a distortion +, very simple and yet incredibly effective. I don't own any other mxr pedals, but have been interested in adding their 10 band eq to my bass board.
How do you find the 78 distortion? I believe that's the one based on the boss ds-1? I've been really interested in trying one, but my GF gifted me a ds-1 a few years back and I've modded it to work better for bass and raised the clipping threshold for less fizz.