Turkish delight: cornstarch or gelatine?
If you want to make real Turkish delight, use cornstarch and only cornstarch. Nowhere on the Balkan have I seen a gelatine-thickened Turkish delight. No Turkish person will recognize a gelatine-thickened candy as lokum. I would go as far as to insist that aromatzied sugar syrup+gelatine = gummi bear, while aromatized sugar syrup+cornstarch = Turkish delight, although some people will feel that this is pedantic. 

Beside authenticity, gelatine-containing recipes are prone to weeping, I have seen questions about that around here. 

Bottom line: I would always make it with cornstarch. This doesn't mean that candy made with gelatine can't be tasty; it is just that if you want what you get in a Turkish shop, you can't do it with gelatine.