I like MDF because it's inexpensive and it's one of the easiest material to work with. Dimensionally, it's very precious. 3/4" MDF is within a few thous of 3/4". However, it's horrible with dust. Its dust is very fine, clings to plastic like iron filing to magnets, and if you don't wear a dust mask, you'll be coughing it out for a couple of days. MDF also requires you to either paint or veneer, so overall, it can be more expensive than BB ply.

BB ply is more expensive than MDF but don't necessarily need veneering, so it can have a lower overall cost. It has pretty heavy sawdust so clean-up is not a big problem. On the negative side, I don't find it easy to work with. Blow-outs, chip-outs, splinters happen pretty easily and can be frustrating if you plan on using the BB ply as the finished surface. The way it takes on stain is also very sensitive to surface prep, so if you're inconsistent with sanding, you will get colour blotches. This is true with any wood but I find BB ply to be very much so.

Gar.