I personally run a sb in my tank and a dsb in my fuge. The reason I do this is I like how the shallow looks in the tanks, and may would argue the surface area of the sand provides alot of places of good bacteria to colonize. The reason I did not do the dsb in my main tank is they are reported to be sulfer sinks they could crash your tank if that sand is disturbed and released into the tank. I do run one in my fuge because if I am getting a sulfer smell indicating a problem may be brewing, I can cut the fuge off from the tank and in a pinch remove the dsb without killing my tank. The big advantage to the dsb is certian bacteria thrive under more anaerobic conditions, and these bacteria can break down nitrates. So the dsb is good for nitrate export.
People who run bb do so mainly because is is easy to clean, and with new sand or crushed coral there is no substrate to release phosphate, or trap unwanted waste products.