Almost everything about Neanderthals is controversial. Take almost everything you read about Neanderthals that talks in absolutes with a grain of salt, because chances are a significant body of reasonable well-respected experts will disagree. The typical story is something along the lines of "well, there is some evidence, but it's not very strong, and it could mean a number of different things, and oh, it also could have been humans".
With pre-historic humans we can reasonably safely operate on the assumption they were at least roughly like us, and take lessons from more recent hunter-gatherer groups, and things like that. But for Neanderthals you can't really do that because their behaviour and "sensibilities" could have been very different.
It was bloody rude of them to go extinct before we had a chance to ask some questions.
In other words, maybe they were high-functioning, it's just possible. But I wouldn't bet on it.
In as much as I can see why "no significant intelligence" is the null hypothesis, I'd still be inclined to word doubts more cautiously. There is a difference between "we don't have strong enough evidence to reject the null hypothesis" and "I think the null hypothesis is more probable."
Personally, I don't think there is all that much mystery what happened.
Animals seem to have this habit of vanishing when humans move in.
A lot of high school textbooks carried a very simplified message about human evolution and basically included neanderthals as 'a branch of human evolution that died out due to being dumb.'
Sci-fi authors actually gave the subject a fairly good treatment, quite a few sci-fi books covered neanderthals and posited neanderthal/sapiens tribal wars etc.
Couple of short stories in the Man-Kzin Wars books cover the subject:
Cathouse (in The Man-Kzin Wars)
and
Briar Patch (in The Man-Kzin Wars II )
both by Dean Ing
Very much worth a read...
When I was a kid I liked Asimov's Child of Time.
One might argue that painting ochre on cave walls is more intelligent (and culturally superior ) than painting radioactivity all over the sky, painting man-made carcinogens all over the ground, painting our insides with plastic, depleting - as rapidly as possible - resources future humans will need ... and all the 'clever' magic tricks we can beat our chests about.
'Modern' may turn out, one day, to be a darkly humorous pejorative.
For all you know, every humanoid species that was intelligent was equally as destructive. Maybe we're the least destructive and you should be praising us.