If aliens were to transport Neanderthals to another planet and we were able to contact their descendants, would they be consider human or alien?
Human, by definition - their full nomenclature is Homo sapiens neanderthalensis (or Homo neanderthalensis, depending on which system you go with). Human, definitely. Homo sapiens sapiens? Of course not. But remember, we did breed with them so, according to our definitions, we're the same species.
The real question is, aside from an academic interest, who cares? If we can learn their language, or they can learn ours (who knows how much they've changed in almost half a million years), it would be easier to discuss things with them than it would be for someone who speaks only English to discuss things with someone who speaks only Turkish - and they could be so close that they're cousins.
Now, if you go to the other end, about 30,000 years ago, we were breeding with them, and unless I have ancestors I'd rather not know about, it was consensual, not forced rape, so evidently we considered them human enough for that. (Not just once in a rare while - our species, as a whole, carries about 20% of their genes, so there was a lot if breeding going on. Look at some of the more famous reconstructions of Neanderthal females [unless you prefer men] - they're not bad looking at all. Definitely human in my eyes.)
Alien? If you define "alien" as "having come from another world", definitely. If you define it as "having originated on another world", definitely not. Are they "modern humans"? No. Heidelbergensis (also known as Homo sapiens paleohungaricus) wasn't either, but he was alive when Neanderthal was - they overlapped. So if Hh is human, Hn certainly is.
It depends on what happened to them on this other planet.
How long were they there?
Was there enough time for them to evolve into a completely different species?
What were the selective pressures on their survival ?
Did the aliens or the Neanderthals(NTs) physically modify the NTs with genetic engineering or some other technology and to what extent ?
As long as they had not been modified to a humanly unrecognizable form we would probably consider them human.
Personally, I think that if we and their descendants were able to communicate on a mutually friendly basis, I believe we would consider them human and an honored group of lost relatives and there would be warmth and acceptance both ways. They might be equally technologically advanced as us, or more so, if we could communicate and many of the world's people have genetic proof of some NT ancestory.
Humans consider other humans aliens or subhuman according to melatonin production levels.
Neanderthals could be hyper-intelligent superbeings with all the answers to all the mysteries of the universe, and there'd probably still be humans who hunted them for food.
If we admitted their humanness, we'd redefine humans to include other species by merit of level of sentience as genetic difference would definitely mean they're a new species and we'd have nothing in common. And that will then include animals actively slaughtered in large numbers on Earth for food. Which won't go down well.
Humans tend to be tribal, us vs them, so classing Neanderthals as alien would be politically easy.
They would be considered both. They are aliens to us since they inhabit a planet that is not Earth, but they are still ancestrally human, no matter how much they evolved, they would still be classed as "humans", in the same way that any descendants of a dog are classed as dogs themselves. The science fiction book All Tomorrows by C.M. Kosemen, takes an interesting, yet disturbing twist on this concept, with humanity's descendants being "humans" but not humanity.