Nasher linked you to the thread I was thinking of, here are some generalizations...I'm sure there are more....
Pro and Con....issues are shown in real time. You overfeed, or have a large nutient input, then you'll see algae. The pro of that is you see it right away...the con, you see it right away.
Pro - much easier to do maintenance on the bottom....you can siphon up the waste and detritus as it accumulates.
Con - you have to keep up with the maintenance/husbandry, or else you will deal with the first Pro and Con listed.
Pro - can have really good flow on the bottom of the tank, without worry of stirring up sand. This can also aid the maintenance aspect of BB tanks.
Pro and Con - aesthetics. Some folks dont like the look of a BB tank, while others don't mind. The bottom gets coated in coralline algae
Con - you can't keep any sand loving critters in a BB tank.