Arceus vs Mew
Those of you who said Mew would win because it is the ancestor of all Pokemon.. you should rethink what you said.
Arceus undoubtedly created the Sinnoh region and possibly the entire Pokémon world, the lake guardians: Uxie, Azelf, Mesprit, and the creation trio: Dialga, Palkia, and Giratina. Because of this, Arceus is thought to be one of the most long-lived and most powerful of all Pokémon species. It has the power to recreate the creation trio as well, presumably to guard the dimensions when a Trainer has caught one of them.
In it's debut movie, Arceus and the Jewel of Life, Sheena said it has enough power to wipe out all of humanity. It's signature move Judgement would crush Mew. Also, using its Plates every attack Mew uses (even if it transforms into another Pokemon, Legendary or Not) will be useless.
Yes, Mew is cuter than Arceus because it's teeny and looks like a pink cat (fetus etc) but Arceus is infinitely cooler, much more powerful, has the ability to create worlds, destroy worlds, and Legendary Pokemon.