Well, let's be civilized here...
Rayquaza: Dragon/Flying
Ability: Air Lock (Prevents weather effects)
Move Types:
Dragon -Twister, Dragon Claw, Dragon Dance, Outrage
Rock -Ancientpower, Sandstorm
Dark -Crunch
Flying -Fly, Aerial Ace
Psychic -Rest
Water -Water Pulse, Rain Dance, Surf, Waterfall, Dive (DIVE?)
Poison -Toxic
Fighting -Bulk Up, Brick Break, Rock Smash
Fire -Sunny Day, Flamethrower, Fire Blast, Overheat
Ice -Ice Beam, Blizzard, Icy Wind
Grass -Solarbeam
Steel -Iron Tail
Electric -Thunderbolt, Thunder, Shock Wave, Thunder Wave
Ground -Earthquake, Mud-Slap
Bug -Fury Cutter
Yeah... That's a lot of typings. The only type it doesn't have is Ghost.
Mewtwo: Psychic
Ability: Pressure (Opponent uses 2 PP per move)
Move Types:
Psychic -Confusion, Barrier, Future Sight, Psychic, Amnesia, Calm Mind, Light Screen, Reflect, Rest, Skill Swap, Dream Eater
Ice -Mist, Hail, Ice Beam, Blizzard, Icy Wind, Ice Punch
Fighting -Focus Punch, Bulk Up, Brick Break, Rock Smash, Counter, Seismic Toss, Dynamicpunch
Water -Water Pulse, Rain Dance
Poison -Toxic
Fire -Sunny Day, Flamethrower, Fire Blast, Fire Punch
Dark -Taunt, Torment, Snatch
Grass -Solarbeam
Steel -Iron Tail
Electric -Thunderbolt, Thunder, Shock Wave, Thunder Wave, Thunderpunch
Ground -Earthquake, Mud-Slap
Ghost -Shadow Ball
Rock -Sandstorm, Rock Tomb
Flying -Aerial Ace
No Bug here, but it isn't much a Psychic would want.
So, honestly, it's pretty close. Your call, man.