Hi, Donna! Personally, I much prefer wafer paper from a texture and flavor standpoint - it's flavorless, but it tends to be thinner and more delicate certainly than Kopykake frosting sheets, which can be thick and gummy. So I find wafer paper dissolves more rapidly on the tongue with less interference with cookie texture.
But frosting sheets (most brands anyway) are more opaque, so less of the underlying cookie will show through them, and the application also looks more "even."
I hope this helps a bit.