+ side to BB is that you get to have everyone bash the look of BB.
Now for what I perceive as real advantages...
1) If/When my tank looses power, I have that much less die-off. Power loss from a tripped GFCI, or Common Power loss. Meaning that I have fewer organisms firstly using less O2, and secondly less polluting when they do succumb. I believe this was one reason I lost my tank years ago when I moved. I contend that a lot of the life in my SB died due to lack of O2 in the water, thus polluting the rest of my tank.
2) I have no fear of left-over foods, or detritus build up anywhere in the tank.
3) Tons of flow. Tons of general flow, throughout the tank. I could not have the flow I do with a DSB.
4) I don't really care about having a completely diverse system. I keep my tank for the corals. That's it. Bio-diversity really doesn't matter to me in my system. Take that with a grain of salt. Of course there is some diversity, just not the abundance that you find in DSB's.
5) No fear of scratching glass/acrylic with that single grain of sand caught in your MAG cleaner!
6) There are others, I'm sure.
Positives of a DSB?
1) Aesthetics of course right? BB is very ugly right?
2) It really does allow you a bit of a cushion I suppose. My first tanks were DSB, and they were bullet-proof for the first 3 years or so. They were also softie tanks that were a little less demanding than a clam/SPS tank.
3) Buffering.... O wait, that's mostly myth. May have some very minor buffering capacity, but not at all what some people preach.
4) If your into bio-diversity then this is totally for you. Tons of works and pods and a slew of other goodies.
My current tank is BB. The bottom is almost totally concealed by rockwork and corraline. I think I have a pretty decent looking set-up, and my corals are happier than ever.