Obviously they are going to be seen somewhat differently, but they should be given the same rights that we have. It is believed that Neanderthals were roughly as intelligent as modern humans on average (maybe a little more, maybe a little less). They are also believed to have looked very much like modern humans, there should be no problem with them fitting in our society.
They would obviously be studied, but hopefully only with the permission of their legal guardian or their own once they are adults. I could imagine them being raised just as any other child (just with a few extra "check-ups").
Overall, with the evidence we have today of what they were like, I see no problem with bringing them back. They were not the half human/half beast creatures that they are often depicted as, they were just a slightly different kind of human (all non-Africans actually have a little bit of Neanderthal in them, there was some "mixing" before they went extinct, they couldn't have been that different for that to happen).
While there are probably many moral and ethical concerns on this, I think we would learn a lot from cloning and reviving the Neanderthal. If it can be done, we should at least have a small trial to see how these hominids function and what their brain capacity is like.
Moral arguments aside, if we could clone and revive a Neanderthal it would be pretty amazing. It would be so cool to see how they move, how they think, interact, even how they really actually look in person. They are like modern humans in some ways, and are very different in others,and to be able to observe that first hand would be great.
How would this neanderthal integrate itself amongst a different species? Would it receive all the rights of a homosapien? Treating an intelligent being as a test subject or experiment is frankly disgusting. Moral arguments aside? No. We can't just push moral arguments aside. That makes us no better than beasts.
The site below lists how scientists believe they vanished:
Why would you want to clone them, they are basically a primitive form of humans, we don't even get along with all the other humans that currently exist. Its not like your bringing back an extinct animal that may still have a habitat you could release them into.
Maybe it is not right to experiment with living creatures inside of science labs or anywhere else for that matter because no one really knows for sure what type of creature the Neanderthal was. He might spread a disease or become violent and he would be out of his habitat and become lonely.
The Neanderthal should not be cloned and revived because it would be unnatural. It is not right for scientsits to play god by cloning species that have gone extinct. Rather, scientists should focus on preserving the current environment so that people today can survive into the future and not also die out.