Mew is cute, and is the "mother" of all Pokemon. It has much more mystery surrounding it's existence. It can learn almost every move is also really cool.
However I have always preferred Mewtwo, and it is one of my all time favourite Pokemon. Ever since the first Pokemon movie, I've loved Mewtwo's attitude and perception of power. When I first played Red as a kid, Mewtwo was insanely strong and he beat all of my friends in link battles and on Pokemon Stadium. I think Mewtwo gave me a bit of a power rush >< Now I collect Mewtwo merchandise, and my Mewtwo on Pokemon X is never let out of Pokemon-Amie. I just love him. Although I do like Mew, I think it is hard to like one and hate the other - seeing as Mewtwo is such a part of Mew.
I must say though, since the new Pokemon Movie which starred "another" Mewtwo, I have been a bit confused about the first Mewtwo. There was literally no explanation of how the new one came to being. I guess we were supposed to just forget the old one, but it's quite difficult seeing as he was so bad ass and evil.