The way I look at it is that Arceus can become any type while Mew can learn any moves.
From my point of view Arceus already got the upper hand as of how it represent all the types while Mew stay put with the ability to learn anything.
My theory would be that Arceus created the world as "God" and sent his "child" being Mew into the created world where it represented all the Pokemon. Meaning that Arceus control the world it created (as said in the anime) while Mew does the inside
job by roaming around the world.