I've spent a little time with each.
The MM is more clear up top and very firm feeling. Some would say "stiff." Between that and the very deep (not hyped, necessarily, just deep) low end, I had to adapt my technique a little bit, but it was an adaptation I was able to make without much trouble. To get the mids where I liked them, I had to do a tiny bit of boosting (don't recall exactly where). The Gain, with my passive bass, was more a signal/noise optimization thing until it got up around 3:00, where it got a bit of harmonic edge and took just a little "edge" off the feel. That's about where I liked running it.
The Bass Block, like the Minimega, has more going on in the deep lows than most micros (again, not necessarily hyped -- at least with the EQ at noon -- but deep). The feel is a good deal looser than that of the MM, the tone, relative to the very clear MM, a bit on the wooly side, however I wouldn't call the amp sloppy feeling or wooly. I played it back to back with a very nice and responsive tube amp (a Shaw B-150) run clean and it does have some of that feel -- better executed in that regard than any other "tubey" micro I've tried -- but it didn't have quite the clarity of the Shaw (which had a beautiful, shimmering top end and crystal clear, slightly compressed lows). The EQ on the BB is broad and simple but well-voiced -- I found it to be effective and musical. There is a nice, propulsive bounce to the feel when playing fingerstyle that makes you want to play loping, syncopated bass lines. Again, while I'm far from an expert on tube amps, I wouldn't say "it's a tube amp," but it definitely takes inspiration from them and incorporates that in a natural-feeling way. Gain affects the feel/compression (or limiting) all through its range.
In terms of tone and feel I could use either amp on a gig and be happy. The MM to me felt just a bit on the harsh/stiff side but was certainly workable and I liked that everything I did with my right hand was clearly communicated by the amp. EQ is very flexible. While I liked the "bounce" of the BB -- it's responsive and easy to play overall -- the feel, for my taste, is just a bit on the loose side. Very fast (well, as fast as I can play them) bridge pickup runs would tend to blur a bit. I found myself adapting my technique with the BB, too, but in the opposite direction of the MM. I'd also like a little more edge/air up top, maybe via something like a "bright" switch or a presence control.
The BB is more forgiving in feel and more old-school in its tonal leanings. The MM is more exacting and modern. Each is flexible enough tonally and responsive enough to technique to cover a wide variety of music, but if I had to play in an Otis Redding tribute band I'd pick the BB and if I had to play a night of Mudvayne covers I'd pick the MM.