Eve is better in the long run, while Elise is better at early/mid game. She's probably one of the best bullies in lane because of her Q, but Eve is a true hard carry, while Elise is more tanky AP, so as the game progresses, Eve will fair better and better until finally she basically has the potential to burst down Elise, while Elise won't be able to keep up with it.
However, a good Elise will still give her a run for her money, as Elise has actual hard cc and a pretty well-rounded skill set. If Elise plays it right, she could possibly wear Eve down before Eve can get her burst on.
So it's an either or for me, but I'd put my chips on Eve solely because it's harder to fuck up as Eve.