The one thing that is bad for society is low diversity. If you become a monoculture, you are at great risk of perishing. Therefore, the recreation of Neanderthals would be mainly a question of societal risk avoidance.

Neanderthals might think differently than we do. They could even be more intelligent than us. When the time comes to deal with an epidemic or getting off the planet, it's conceivable that their way of thinking could be beneficial.

If society becomes comfortable with cloning and sees value in true human diversity, then the whole Neanderthal creature itself could be cloned by a surrogate mother chimp - or by an extremely adventurous female human.

George M. Church Quotes