I use the curly, copiously in quinoa tabouley. The taste to me is better. Also, the texture, the way it has spring to it, and feels *cleaner*, and *greener*.
Recently I tried the flat-leaf in a kind of perogi-affair, made with a barley dough.
It seems to me people like it - the flat- cooked IN something. In this case it was potato with lots of spices and chilis, and cilantro. I don't actually think much of the flavour. Very flat and almost plastic.