The advantage of 1-3-1 D is that the perimeter D will be superior to 3-2 D. but on the other hand, the rebounding will be much lower than 3-2 D.
The advantage of 3-2 D is that it gives (most of the time) more rebounds than 1-3-1 D.
I don't have enough knowledge to answer other questions, but if you're playing a team that has a ridiculously good outside shooting and horrible rebounding, 1-3-1 D could work. But in my opinion, 3-2 D is better than 1-3-1 D, because 1-3-1 D will give the other team too many offensive rebound and they could get extra points from that.