Battles

@SpeedForceSpider: He didn't created Deoxys, he didn't created the Castform, Mewtwo doesn't count (I don't even think he is consider a Pokemon), he didn't created the Legendary trio of Johto... Ho-oh did (but that could be a myth).. but besides those yes he created all Pokemon...

and for this Battle... Arceus still wins...

@SpeedForceSpider: Here is almost everything you need to know about Mewtwo. http://www.smogon.com/rb/pokemon/mewtwo

If you need anything else, tell me. Just reminding you, I'm not saying Mewtwo guarunteedly wins, but I am saying that it's not a stomp. Mewtwo also has a higher base Speed (130) compared to Arceus' base speed (120). Here is Arceus also. http://www.smogon.com/bw/pokemon/arceus-normal

@TheBlackDragonz: Pretty impressive, but even Lugia has better stats than Mewtwo in a some areas. Arceus literally has a perfect balance of stats, knows all moves, and can change his type. I just can't see Mewtwo comparing with just a slight speed boost. So yes in fact, This is most likely a stomp.

@SpeedForceSpider: But, with what? I understand very clearly that neither is stomping the other, but what does Arceus have that Mewtwo should worry? As Mewtwo is faster, it is able to use Amnesia to boost it's own special offensively, and due to being RBY Mewtwo, resistance to incoming special attacks also. Something else from the same site is right here:

Type Differences

There are a few differences when it comes to a type's effectiveness against another type in RBY.

• Ice attacks are neutral to Fire instead of not very effective.
• Poison attacks are super effective against Bug instead of neutral.
• Bug attacks are super effective against Poison instead of not very effective.
• Ghost attacks will NOT work on Psychics instead of being super effective regardless of what any RBY type chart tells you

So, ghost Arceus won't work, Dark and Steel Arceus don't exist for RBY Mewtwo (this is because RBY Mewtwo doesn't have a weakness to Dark in it's programming, as well as his attacks not being programmed to be not-very-effective on Steel.) So, pretty much all Arceus got for Super Effective is Bug-Type Judgement. And then, like I said, there's the aforementioned Amnesia that can weaken the damage it does while also boosting what Mewtwo can do in return.

God > Strongest Mortal ?

@ohgodwhy: 
I don't even think he needs it. Mewtwo in RBY can learn Submission. Although a physical attack, it is still pretty powerful on Mewtwo and can probably mess Normal Arceus up pretty badly. Mewtwo also has access to moves such as Reflect, Barrier, and the beast that was known as Hyper Beam. An alternate way it could go is: 
 
Turn 1: Mewtwo Reflect/Barrier 
Turn 2: Arceus Swords Dance 
Turn 3: Arceus Extremespeed  
 
Mewtwo will most likely live. 
 
Turn 4: This depends on how much Extremespeed does. Mewtwo can then use Disable, Recover, Thunder Wave, or whichever move he didn't use in Turn 1. 
 
But most of all, On turn 4, if Mewtwo lives that Extremespeed, he has access to Counter. Let's see Arceus live it's own blast at double the strength. 
 
(Sorry if I'm coming across as harsh, but I'm seeing this debate as becoming some Serious Buisness, here.)

Mewtwo will catch Arceus in a Master ball and win... lol

since he is the only pokemon to show that has used a pokeball before.. (movie 1)