I have never been to London, but have spent ~2 months in Paris while I was doing research there. I absolutely loved Paris, and it would be great to live there....but that being said, Barcelona is the most fun city I have been to in Europe. It is so much fun - if you are into the night life and like going out to bars/clubs - and it is a lot of fun to see people start to go out to dinner at like 10:00pm or later.
Depends on what you are looking for, but if you want sheer fun, I would say barcelona....of course, if you are more into musuems and historical sites, I think paris wins, despite all the gaudi stuff in barcelona.