I longarm quilt and use two layers of batting quite often. I usually mix with a "denser" bat on the bottom, like W&N or Hobbs 80/20 QD cotton and once I did a wool army blanket. The top batting I use the loftier batt. I have used wool on top and also Hobbs polydown. I would not attempt doing this on a sit down set up be it a domestic or one of the larger harp sit downs like an HQ16. I just can't imagine trying to manipulate that kind of weight and bulk around. On a rack I don't have to worry about weight, bulk or shifting of all the layers.
Pros: Great definition to the quilting. Really makes it show. Quilt is super warm.
Cons: Quilt is much heavier weight wise.
Drape I have found really varies with the size of the quilt. Most bed size quilts I have done with two layers still drape on the bed very nicely and are not stiff, but this is really a matter of opinion. What one person thinks is stiff another person may not. I have found that smaller pieces like wall hangings are stiffer but given that the size is smaller what is there to drape? The stiffest was the one I did with a wool army blanket. That quilt lays on top of my bed in winter and I have it hanging the rest of the year. It is super warm but is also not real cuddly but that is ok with me because the quit is still very beautiful and very functional.