The strength of a bb tank is the control that the reefkeeper has over the tank's parameters. If you are just keeping LPS and softies control doesn't really matter. You can keep those corals alive in a 5 gallon bucket. On the other hand, if you are keeping SPS then having control becomes a bigger deal(I would say that the control of the colors is the source of the fun for me). The rest of this post regards sps tanks.
Once you have figured out how to keep the basics (temp, salinity, alk, calcium) under control, there are only 2 parameters that an SPS keeper needs to adjust. One of them is the lighting, and the other is feeding. Longer/more intense photo period will lighten corals, and heavier feeding will darken them. Finding the right combination is how you acheive success. The adjustments are easier to make in a bb tank, because there is no semi-constant (sand bed) leaching or absorbing nutrients. If I reduce the feeding in my bb tank, the nutirent levels drop quickly and the change in the corals is obvious in no time. In a tank with sand, the adjustment of feeding has less of an effect, because the sand bed is the product of past water quality and will continue to effect the tank after changes are made. The claims made in above posts that the sand creates another ecosystem and thereby food for fish and corals is exactly why I prefer a bb tank. It really is a simple as that.
The control you have over water quallity with a bb tank comes at a price. The tank is less forgiving. On the other hand, if you do a big water change in a bb tank, your new water quality is completely independent of your old water quality (except for the effects of the rocks which is where rock cooking comes in to play). In a tank with a nutrient loaded sand bed, a big water change will have less of an effect because the sand bed will come back into equilibrium with the water, thereby reducing the water quality. So although the bb tank is less forgiving of day to day stuff(ie keep a very strict routine) it has a greater ability to be put right quickly. This is one of the main reasons why the original bb proponents (bomber etc.) preferred bb tanks. They were keeping tanks that were far too large to be torn down and reworked when their sand beds became overloaded. This is not as much of a concern on a 40gallon breeder.
Obviously there are tons of great tanks that have sand beds and that are bb. Either method works. One just has more control and costs more to set up properly. Some people like the look of sand beds, others like bb. Of course, in an sps tank neither a sand bed nor bb is at all natural looking. So, looking to nature as your inspiration is a bit misguided. Let's just be honest and admit it is personal preference.
Brad