I've never made either, but I'd go with the cornstarch for two reasons. First, the first recipe I found on the BBC site, which I trust, uses cornstarch (they call it "cornflour"). Second, using cornstarch will make the Turkish delight vegetarian; thus, more people will be able to enjoy it. ;o)
Thank you! Great point, will try the cornstarch method :)
I can't comment on the 2 different methods, but here's one recipe for you to consider: https://food52.com/recipes...
Good luck! I've only made it once, using cornstarch and the better part of a day. It was quite a project, but it turned out great. If you have the time and the stirring power, I think that's the way to go.