The 6 part series sharing the same title finished this I thought :) X-Men beat Avengers. No-one in the X-men is a normal human being. 1/3 of the Avengers are.
That being said, assuming the Phoenix Five did not exist, I'll bat it around some more.
X-Men have Omega level mutants on their side. Iceman, Phoenix, Legion, Charles Xavier, Unstoppable Colossus, Franklin Richards, Emma Frost, any variation of clones/children of Scott Summers and Jean Grey.
These characters are beyond powerful. Legion can warp all of reality people. REALITY. Just change history, science, physics, and properties. Some of these are the top telepaths in our galaxy. With concentration and the reasoning to will so, they could wipe the minds of all the Avengers, make them believe they are actually small children, or simply hide the world from them. Phoenix is a world destroyer. What happens when you take control over every water molecule on the planet and freeze it to absolute zero? Iceman destroys the world is what. This is just the X-men, not even all their allies that would help out if the circumstances were right and of course those allies.... many are Omega level as well.
Avengers. They just don't have enough high powered characters to down them all. They would likely try and find a scientific way to take the powers away, but not everyone's powers are the same on the X-Men. You want to take out Professor X's mutant ability? Fine. Let's make it happen. All mutants are without powers, and let's say this somehow didn't effect the Avenger's mutant, Hulk. You have people like Magik and Unstoppable Colossus whose powers are magical in nature. Phoenix is a deity level character. A god. Maybe magical? Avengers' big players are Scarlet Witch (IF she is counted on the Avengers team this time), Hulk, Starbrand, and Dr. Strange.
Dr. Strange = Magik
Starbrand = Legion
Though Franklin Richards never officially joined the X-Men, he was looked after by them for a time. If he was not with his family, he would likely side with the X-Men. Reed Richards is heartless and has been the catalyst for world disaster over and over. I think Franklin would see this and listen to the voice of reason, which would likely be coming from within his mind and voiced by Patrick Stewart.