The problem with Twilight vampires isn't that they sparkle in the sun instead of spontaneously combusting. (The latter was a Hollywood invention anyway. Prior to that, vampires couldn't use their powers during the day or just didn't appear except at night. Either portrayal is valid, I think.) No, the problem with Twilight vampires is that they have all the advantages of being vampires that have come to be considered staples in vampire folklore--and then some!--but no disadvantages whatsoever. They have to drink blood, but it can be animal blood, so there's no ethical issue with being a vampire. They aren't harmed or inconvenienced by sunlight, garlic, stakes, fire, running water, or poppy seeds. They don't have to sleep in coffins or underground--don't have to sleep at all. They look completely human, in fact they look like the most beautiful humans in existence. They live in happy little functional family units and have awesome sex lives and play superhero baseball. There is literally no downside to being a vampire in the Twilight continuity.
And that? Ruins vampires. The legend of the vampire has come to symbolize the conflict between certain very human desires--the desire for power, for immortality, for freedom from the constraints of human society--and the suspicion that in order to have those things, you would lose the parts of your humanity that you would rather keep. You can't live forever unless you steal life (blood) from others. If you are the lord of the night in your remote castle, then you have no friends and no love and keep company with rats and bats, and daylight itself is your enemy. You transcend your human frailties only by abandoning humanity altogether and becoming a loathsome monster.
Without that angle, vampires become shallow and pointless. The Twilight creatures are called vampires because vampires were already kinda trendy when Stephanie Meyer was writing, but they aren't really vampires in any meaningful sense of the word.