Which X-Men universe are we talking about vs which Avenger universe? There are plenty of twists and turns based on the answer to that question and since I can assume that many of the users posting here have not read the entire story lines (myself included), I'm going to assume that the op along with some of the other posters have only seen the movie/cartoon series.
Avengers: Yes, the avengers have a god on their side in Thor. He is quite formidable but far from invincible. If you read the comic series you know that Thor isn't immortal and in his best form (warrior's madness) his strength is enhanced, but it's a bit like berserker mode. Thor attacks all parties around, friend and foe. This flaw makes Thor a wild card if he is pushed to his limit. Finally, Thor's weakness is magic which can transform him to mortal status.
X-Men: The Phoenix first off was born in space so she can indeed breath in space. She has the ability to resurrect from death many times (this has been supported via the comic series) which is probably why she is named the phoenix. While Jean Grey is using phoenix force she can rearrange molecules on a atomic level, who can really contend with that? Now how about an ultimate weapon, using phoenix force can take the life energy from one and give it to another, which can fully heal or even resurrect that individual. Rev anyone?
Wild card: Rogue at her best had the ability to fly as well as super human strength but her greatest asset has always been the ability to steal any memory, skill or power from anyone (human or sentient being) through touch. For the duration she is in possession of these things the original owner is without, and if she sustains contact for a prolonged amount of time the transfer is permanent. So basically she can nullify Iron Man's intellect or even Thor's god-like status and have immediate mastery over the newly obtained ability.
A quick read in Wikipedia will support all of the information above: Thor/Jean Grey. Sorry to rain on that parade, I have no idea what is going to happen in the comic series, but as far as mutants goes, Jean Grey with control of the Phoenix is pretty tops imo.
I just hope that Thor and Wolverine get to go toe-to-toe; warrior's madness vs berserker mode, everyone back up and let them have at it. That battle would rage on forever since they both have regen capabilities, I might give a slight edge to Thor based on his abilities, but Logan has fought some of the of the world's fiercest heroes and villains. I wonder if Wolverine is actually teamed up with the X-Men or Avengers (he has been affiliated with both units).
Based on the these units above: I would think about giving the edge to the Avengers since Jean Grey isn't pictured. Thought the picture depicts 7 vs 6, two of the Avengers (Hawkeye and Black Widow) are just humans are fairly useless against a team of mutants imo. Iron Man may be nullified by Magneto, it's also notable that Mjolnir (Thor's hammer) is made of uru which is Asgardian metal. Not to mention Thor is decked out in all of the finest warrior armor, which is basically prey to the master of magnetism. Once Thor is nullified, the Avengers are pretty much worthless. Cyclops and Captain American are pretty much on par. Black Widow and Hawkeye are dead instantly. White Queen is can manipulate her structure to be hard as a diamond so she could potentially go blow for blow with the Hulk, plus can also use telepathy to control members of the Avengers (but cannot do both at the same time). Finally, Spider-Man is probably the number 2 in the Avengers imo due to his intellect, healing factor and Spider-sense to alert him to danger, too bad that the X-Men still have Storm who controls the elements (and has an affinity for magic which is Thor's weakness btw) and Namor, who I never really liked but he is strong/fast and can fly.
Side note: If you read some of these profiles you'll notice that Logan (Wolverine), Namor and Storm have each been a part of the X-Men and Avengers; and a also partnerships between Spider-Man and Wolverine. As I said before, in the end it'll come down to who is on which team; if Thor is in, Jean Grey out, green vs red Hulk or Colossus with Juggernaut powers... the line ups are limitless.
*There are plenty of wiki links in this post, feel free to study up. Wikipedia may not house the most accurate information on the web but when it comes to fanboys and their comics, false information won't be up long.
**How's that for research Thren? This entire work was research due to the fact that I've never read a comic book in my life, everything I know I learned via video game, word of mouth and Wikipedia.