Kirito loses because everyone hates SAO.
I kid, but Adrien seems to have a faster reaction speed, higher range with his staff, and better lifting strength with just using his staff, thus more accelerated power when doing a pull attack. Kirito has some regen though that could render all of the damage he takes pointless.
With lethality of weapon, Kirito can cut and has access to two swords (can block and strike given sufficient range, but
IRL dual wielding may not be that strong), where one cut is probably more lethal than a brutal strike by a staff on the arm (either should disable though). Adrien has to land a pretty hard strike for damage, and given his extremely high "lifting" power with the staff, has true three-dimensional control of his staff. With similar strength, I think Kirito has to resort to one blade kendo style to match the double-handed strength of the staff. Range goes to Cat Noir, a lethal strike by Kirito can be avoided.
In close combat, that extra reaction speed, ability to react and brush his staff (a pull movement) with equal push striking power and longer range could tip Adrien in favor, but I'm not sure with speed equalized that would help him land an attack unless his staff is up in Kirito's face, given that their striking speed is likely not supersonic level. Kirito might be able to run up, take a blow and cut Cat Noir up (though Cat Noir can probably react just in time for a Cataclysm). Better control of the staff along with better reaction speed goes to Cat Noir once again.
I'd say Cat Noir has the advantage in fighting, but the healing factor for Kirito makes it interesting. I don't know if Cat Noir can disable/disarm and annihilate Kirito fast enough, and not just get off a few scratches. I also don't know how long Cat Noir can extend his staff (if it's infinite and Cat Noir can control a 100m+ long staff, he can make enough distance away from Kirito and strike much faster at a further distance due to basic mathematics). I would give it to Cat Noir if an infinte length staff was available.
