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It's like comparing an eleborate cake with edible crystalized gelatin flower decorations to a rock. Harry Potter is the cake and Twilight is the rock. Or you could compare Harry Potter to Twilight like a boulder to a pebble, respectively.
Twilight sucks balls.
Twilight is full of plotholes, and questions are left unexplained. Harry Potter ties up all loose ends and explains everything thoroughly.
Twilight has fake, fantasy, flat, bland, and unrealistic characters. Harry Potter has realistic characters with realistic problems and realistic issues, and the romance in Harry Potter is realistic.
The only drama in Twilight is when Edward leaves and when Bella dumps Jacob. The drama in Harry Potter is when Cedric dies and Cho Chang finds comfort in Harry, when Harry and Cho break up, when Hermione watches Ron and Lavender make out, when Lupin didn't want to marry Tonks due to his age and him being a REAL werewolf, all the drama between Snape and Lily, when Dumbledore dies, when Sirius dies, when Lupin and Tonks die, when Hedwig dies, when Mad-Eye Moody dies, when Harry brings Cedric's body back, etc. The list could go on and on.
A long story made short, Harry Potter crushes Twilight to the ground.