What is more interesting or powerful: Curry, Mercury or Lambda-Prolog?

Twelf.

It generalizes lambda-prolog significantly, and it's a logical framework and a metalogical framework as well as a logic programming language. If you need a language with a heavy focus on logic as well as computation, it's the best I know of.

Prolog was the first language which changed my point of view at programming. But later I found it to be not so high-level as I'd like to see it.

Curry - I've tried only Munster CC, and found it somewhat inconvenient. Actually, at this point, I decided to stop ignoring Haskell.

Mercury has many things which I wanted to see in Prolog. I have a really good expectation about the possibility to distinguish modes of rules. Programs written in Mercury should inspire compiler to do a lot of optimizations (I guess).