Um, no. We belong to the same genus not species. Assuming that is what you meant, what exactly are the concerns of cloning a human? Most arguments I hear typically involve a religious appeal and we all know how well science and religion mix. Aside from that, I am not so sure any religion would be quick to embrace a living Neanderthal. The best argument I could think of against cloning a Neanderthal would be the concerns I have for it's health and happiness. We know very little of the culture, diet, needs, or temperament of Neanderthals. On the other hand, we do know what a good diet consists of and what generally makes humans happy. Our cultures are rather well studied too. A cloned human living a healthy and happy life doesn't seem far fetched to me. I am not so sure about the Neanderthal. None of this means I would rush out and clone humans or Neanderthals but I will say the concerns are not the same.
Actually, you just described a subspecies... Different species don't interbreed, that is part of the definition. The argument in the scientific community is whether or not neanderthal and sapiens bread together, in which cause they would be of the same species and different subspecies... you are a homo sapiens sapiens
If you can count your money, you don't have a billion dollars. -- J. Paul Getty