I have played Dota 2 only once and I didn't quite like it. The user interface was quite confusing and I could barely find my champion on the screen. Maybe I'm just used to League of Legends, but there must be a reason for it to be so much popular. Champion-wise, you need to work a lot on buying the champions in League of Legends, while in Dota 2 you have all of them available, but I don't think that's necessarily a bad thing. I would assume some Dota players are led by what's trendy ("OP") right now when picking their champions and can fail horribly, while League has the element of anticipating the buying of your desired champion and I like that.
LoL is the best.