Other than the price, is there any appreciable difference?
In my experience, not really. Arrowroot is supposed to be a bit clearer than cornstarch, but you’re not supposed to use it with milk because the texture it makes when used with milk isn’t as good as cornstarch. Also, when adding a cornstarch slurry, you need to boil it for a little bit to get rid of the starchy taste – you don’t really need to do this with arrowroot.
However, I really don’t find that much a difference between the two, and use them interchangeably, with a slight preference to arrowroot.