Short version: when you're dealing with someone else's work, it's not a good idea to say "Oh, my creation is (the true one/so much better/not as lame)".
This came to me during my fistfight with Brian Corvello's "Operation: POWERPUFF", but it's bothered me for a very long time now. For some reason, when people are working with someone else's universe, they feel obsessed to declare that their creation is superior.
I don't speak solely - or even primarily - of fanfiction here. Gregory McGuire has made a career out of taking apart other people's work, most notably with his Oz "reimaginings". Never mind that he doesn't seem to know whether he's working with the movies (where the Wicked Witch - I refuse to call her by his name for her - was green) or the book (where she was blind in one eye, a detail that vanishes from Wicked utterly after it's mentioned, incidentally).
It isn't just him, either. I recall reading a summary for a book (I believe it was The Looking-Glass Wars) that had Alice complaining about how Lewis Carroll mangled the Truuuuuuuuue Stoooooooory when he wrote "Alice's Adventures in Wonderland", and the recent Dracula "sequel" has Bram Stoker presented as a fool who screwed up the Truuuuuuuuuuuuue Stooooooooory. With time, I could probably give you a hundred examples.
(I'm separating out, say, vampire stories where the vamps complain about Bram Stoker getting details wrong; that's a different topic for a different day, and I think
zelda_queen would have more to say on it than I would.)
Where fanfiction comes into this is with the "MY CHARACTERS ARE BETTER" angle. Let us consider "Operation: POWERPUFF" again.
In Mr. Corvello's story, there is a character named Lotus. She is the former teacher of Numbah 362, the head of the Kids Next Door in canon, and also taught Chad, one of the villains (whom she repeatedly insults). During her time on the KND, the Decommisioning Officer was a boy whom she proclaims was much nicer and more respectful than Numbah 86.
This is a textbook case of "My characters are BETTER THAN CANON". She's a better swordfighter than the head of Global Command (implicitly, since the teacher is always better than the student), and the staff during her KND days was better than the canon staff.
This isn't just the typical Mary Sue, either. This is when the characters are explicitly compared to canon. Consider, from the same story, Snowball, who is presented as having sabotaged the canon villains from The Powerpuff Girls. This weakens the PPG in comparison, since it implies they couldn't have won without her help.
Another, even more disgusting example comes from one of Corvello's Yu-Gi-Oh fanfics, "Dark Messiah". There, his villain, Sin, is presented as having tempted Kaiser Ryo from GX to turn evil. Given that Hell Kaiser is one of the few villains not explicitly tempted by an outside source in canon (let's just forget that hash of a final season for now...), this ruins the character and exists only to make Sin look good.
This sort of activity reeks of ego. In the former cases, to present your work as being the Truuuuuuuuue Stooooooory is to by extension attack the original's author. In the latter, you are instead attacking the source material itself. In either case, you present yourself or your work as being superior to the original - a claim that, nine times out of ten, is just false.
Let us put an end to this practice. Or at least, if you're going to say your story is better than L. Frank Baum's, it had better damn well be better.