You guys are nuts. I love The Matrix and I'm not a big fan of Supes at all, but outside of the Matrix Neo has no chance. Inside the Matrix the best he can do is stalemate Supes and even that's a stretch.
His only substantial feat outside of the Matrix was destroying a couple hundred sentinels in the Machine City with TK. He eventually tired out though, stating that there were too many of them. So I don't think he'd be able to telekintically hold Supes, like Jplatinum claims. Supes is still completely invulnerable to anything Neo could do to him. Neo would literally break bones in an attempt to hurt him. Hell, Smith hurt Neo horribly after taking over Bane's body. Imagine the 1,000,000 + ways Supes could kill him.
Jplatinum also claims Neo has a stronger will than Supes...I'll leave that one to Supes' fanboys.
"Realistically, he should have the same powers as Smith (as Oracle described him as being his exact opposite-negative if you will) so I can see him taking over bodies. Plus NEO is able to go intangible. Remember when he restarted Trinity's heart? He went semi-intangible and put his hand in her body, and had to materialize it, so he could start it again...which is why she was in severe pain. I wouldn't doubt if his abilities were on par with Agent Smith's."
I don't see how any of this helps him defeat Supes in the Matrix. His ONLY hope is to copy Supes, but he'd have to catch him first, which should be impossible. Supes is infinitely stronger, faster, and more durable than Neo. Supes is also not a program so he can't be deleted. Lastly we have no proof that Neo going intangible could even hurt supes in the same way it did Trinity. So how does he hurt Supes,even in the Matrix? Let's look at what we have so far:
"Against superman Neo can win by various methods:
Beat him to death using his powers and his superior fighting skill"
Neo does has infinitely better H2H, but he'd still break his hand striking Supes.
"Use telekinesis to hold him still with his superior will power"
As stated above, this is a joke.
"Jump inside him and blow him apart from the inside out"
Agent Smith was a program, therefore vulnerable to such an attack. Supes is not a program.
"Delete him from the matrix"
Again...Supes is not a program, therefore he can't be deleted.
"Mentally control him and make him fight his self"
Neo was never shown to have any TP.
"Create mental kryptonite and cark is done"

is "mental kryptonite"? Maybe Neo could write a program for kryptonite. But he can't do it from inside of the Matrix. If he's outside ands Supes is inside, he could actually cause Supes to believe Earth is one big kryptonite rock. That would obviously work. Other than that he's done.