In Battle: Mew, better move choices
Your Personal Favorite: Mew
Who Has The Better Ability: Mew; Synchronize makes status moves backfire, while Celebi's Natural Cure means you have to switch. If it's a 1v1... Celebi's helpless against status.
Who Has The Better Typing: Mew, less weaknesses
Who Is Harder To Obtain: Celebi, since it only appears in GSC and HGSS for events.
Who Has The Better Design: Mew; pink cat thing > bug/sprite thing