First of all, I am an Otaku first and a gamer second, and many community members already know this, so it's no surprise that this would be my favorite/ideal anime crossover!
Sword Art Online vs. Log Horizon!
Sword Art Online
Even though is not the first one on it's genre (.hack series was the first biggest gaming anime, it's pretty awesome as well), SAO basically popularized the "Gaming Genre" in anime with awesome characters, skills, story and world. SAO was all about skills and character development and obviously, beating the games.
Another great gaming anime along side SAO. Personally, I liked LH more than SAO just because it has a more strategic point of view. Unlike SAO, LH focuses on Raiding and co-existing with NPC's (Non-Player Characters) so a lot of teamwork is needed. Furthermore, the players create a government with laws and have massive wars with NPC nations.
Let's get this out of the way: "Kirito would kick Shiroe's ass if it was a 1v1 fight, but on a team fight Shiroe and his party would kick any SAO party". Now that that's settled, I think it would be amazing for both sides to learn about each other.
> One can log out, the other can't.
> NPC's have a mind of their own in LH but not in SAO.
> Different Worlds, jobs, skills, lifestyles in-game, etc.
Furthermore, it would be amazing having Shiroe's flawless commands and Kirito's unmatched skills fight hand-in-hand! These two could basically rule the gaming world. Also, I have always been curious about the real life images of Log Horizon characters and with SAO's help, I could finally get a glimpse of them out of the game (especially Akatsuki >w<).
I hope my dream of seeing these two together at LEAST once, comes true before I die.
Hope you enjoyed it, and I can't wait to see the crazy crossovers you'll all come up with!