There's no contest. Arceus is the most powerful and is the so called "God" of Pokemon. Mew is essentially the first pokemon to naturally evolve and is not "godly".
If we think of Arceus as God, then we can think of Mew as the first natural life form on Earth. Arceus has never been said to 'contain the DNA of all Pokemon' and Missingno has never been shown as 'the God of Pokemon'. MissingNo# was a programming error in the games.
Technically, Mew should not be able to transform into Palkia, Dialga, Giratina, Arceus, Porygon, Heatran, Azelf, Uxie, Mespirit, Groudon, Kyogre, Rayquaza or the regis, as they did not evolve from it.A timeline of Pokemon goes like this:
Arceus is born from an egg in a void of nothingness.
Arceus creates Palkia and Dialga (and most likely Giratina) from itself, and gives them the ability to control time and space. Giratina is banished to the distortion world for its violence.
Arceus then creates Azelf, Uxie and Mespirit to create willpower, knowledge, and emotion, and they dive to the bottom of Lake Valor, Lake Acuity, and Lake Verity.
Various processes in the universe cause the Earth to be formed and Mew evolves either by itself (from early mixtures of chemicals etc ) or with help from Arceus, and contains the DNA of almost all future Pokemon. Earth at this point has little solid ground or water.
Groudon is formed in the magma deep inside the Earth, Kyogre is formed by deep sea pressure and Rayquaza is formed by minerals in the ozone layer. They begin to create land, water and possibly air respectively.
Groudon and Kyogre fight for dominance of earth, which carries on until Rayquaza calms it. Groudon and Kyogre retreat into their special caverns. The blue and red orbs are created to prevent them from fighting again (possibly by Arceus) and Rayquaza starts to fly around the ozone layer.
Regigigas (either formed by the land, evolved from Mew or created by Arceus) moves the continents, forming the Pokemon regions. As Stark mountain is created, Heatran is formed by lava.
Arceus creates the Adamant, Lustrous and Griseous Orbs before falling into a never-ending sleep. (The history in the movie is much different, claiming that Arceus does not sleep until many years later, in which time he protects the Earth and its people).
Mew evolves many times.
Prehistoric Pokemon appear and the Mew population decreases.
The first humans appear, create Regirock in the stone age, Regice in the ice age and Registeel in the iron age, possibly from a special metal from another planet.
Regigigas is sealed away in Snowpoint Temple, and Regirock, Regice and Registeel are sealed away in the Hoenn region.
Humans and the Unown somehow link to the first system of writing.
700 years before Generation I, Tin Tower and Brass Tower are constructed in Ecruteak City, and Lugia and Ho-Oh (evolved from Mew) perch at their tops.
150 years before Generation I, Brass Tower burns to the ground, killing three Pokemon inside. Lugia flees to the Whirl Islands, Ho-Oh resurrects the three dead Pokemon as the legendary beasts and flies off in search of a pure-hearted Trainer.
Porygon is created as the first artificial Pokemon, although not the first made by man.
Mewtwo is cloned from Mew.
The events of all the games take place.
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Things You Didn't Know About Pokemon!
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