You do get some flavor benefits from cooking with the tail on, just like you do by cooking meat on the bone vs. removing the bones. It makes the shrimp more shrimpy which helps the shrimp stand up to rubust flavors like those found in Fra Diavole.
As for when its appropriate to serve tails on, I've always used size of the shrimp and final application be the judge. If the final application is to be mixed in to something else, like rice or pasta, I remove the the tails, but if the shrimp are to be laid on top of something, I would typically leave the tails on. It is alway approiate to leave tails on if the shrimp are large and not a good idea if the shrimp are small, as tail removal is hard to do in small shrimp after cooking.
Another point is that if it is intended to be consumed with the hands, you should leave the tails on as they give you a very nice handle to grasp and eat from.
Soups and anything else that is intended to be eaten with out a knife beside it should be served tail off to facilitate easy consumption.
And it is normal for Fra Diavole to be served tails on.