Since these are both event exclusive Pokemon, I assume you intend to use them competitively. As such I would definitely go with Meloetta :P
Seriously, though, both Pokemon have different strengths and weaknesses, so it depends on what you want.
Mew
This is an extremely versatile Pokemon, that can act as a support Pokemon, a physical sweeper, a special sweeper, or just about any other role you can think off. It does this because of its balanced stats and access to every HM, TM, and Move Tutor move in the game.
Support sets like to run Thunder Wave, Stealth Rocks, and Knock Off, or sometimes Reflect or Light Screen, Heal Bell, and the list goes on.
Physical sets use moves like Swords Dance, Zen Headbutt, Earthquake, Stone Edge, Drain Punch, Seed Bomb, etc., etc. - you get the idea.
Special sets use moves like Nasty Plot, Psychic, Psyshock, Aura Sphere, Thunderbolt, Ice Beam, Flamethrower, Shadow Ball, Flash Cannon, etc., etc - again the list goes on.
From this it is obvious Mew can pretty much be anything you want it to be. It does have some weaknesses, though. As a pure Psychic type it is weak to the very common Ghost type, and also once it has used its first move, you can pretty much guess which set it is running, if not the specific moves on that set.
Meloetta
So after I said all that about Mew, what does Meloetta have to offer? Firstly, its typing means it is immune to Ghost, so that is a definite bonus. Secondly, it gets an alternate form, which gives it nearly as much diversity as Mew has.
Special sets keep it in its base (and arguably weaker) Aria forme. In this form it is Normal/Psychic, and a Special Attacker. Give it moves like Psychic, Hyper Voice, Thunderbolt, Energy Ball, Dazzling Gleam, and so on. The Choice Scarf is generally a good item for this set, because its Speed is not really that good.
Physical sets all need to have one Special move on them - Relic Song. This Normal type move allows Meloetta to transform into its arguably more threatening form - the Pirouette Forme. It is more threatening mostly because of the boosted Speed stat, which is even higher than Greninja's and Talonflame's Speed. In this form it is Normal/Fighting, and its Attack gets a major boost, so it might use moves like Close Combat, Acrobatics, Stone Edge, or U-turn.
Mixed set is the last option here. This pretty much a mix of both sets, where you use Relic Song to keep the opponent off guard, and when in Aria form hit with Psychic or Thunderbolt, and when in Pirouette form hit with Close Combat or Stone Edge. Of course, you do only have 4 move slots, so will need to pick the exact moves you want to use carefully.
Edit
I just looked it up but apparently Meloetta-Pirouette is the 9th fastest Pokemon in the game, excluding Mega's and the different forms of Deoxys. Who would have thought?
Conclusion
Now that I have said all that, which one should you choose? Well there is no clear answer here, and it depends on what you need. Hopefully reading through the descriptions I have given of the two Pokemon will help you choose which one you prefer. Personally, I would go with Meloetta, simply because I like Meloetta. But in my Pokemon Y game I have both a competitive Meloetta and a competitive Mew, and they both work very well.
I hope this helped (somewhat).
