From the BBC article:
"Given the ongoing revelations of Neanderthal art and technology, it is difficult to see how we can regard Neanderthals as anything other than the cognitive equals of modern humans," the study said."

In the case of the study, the string is a short one. They did convince me, however, that Neanderthals were the cognitive equals of some archaeologists. There is a longer string of biological evidence that points to the opposite conclusion of this paper and since the authors were unable to refute it, simply used the Neanderthal method of ignoring it.
The longest string:
[www.smithsonianmag.com]
"Neanderthal brains had more capacity devoted to vision and body control, with less left over for social interactions and complex cognition"

[www.evoanth.net]
"However, FOXP2 isn’t the only gene linked to language. CNTNAP2 is linked to language development in children, whilst ASPM and MHC1 are associated with being able to pick out different tones. And these 3 other genes are absent from Neanderthals6! On balance it would seem that the genetic evidence does not support the idea that Neanderthals had fully modern linguistic capability."

[www.huffingtonpost.com]
"Four years after scientists discovered that the two species' genomes differ by a fraction of a percent, geneticists said on Thursday they have an explanation: the cellular equivalent of "on"/"off" switches that determine whether DNA is activated or not."

[theconversation.com]
"In other words, natural selection would have largely weeded out the Neanderthal-human crosses because their mixed-up genomes led to a reduction in survival and reproductive success. Hybrids were selected against!"

[fire.pppl.gov]
"An additional criterion is whether a “cultural pattern” can be detected, says team member
Shannon McPherron, an archaeologist at the Max Planck Institute for Evolutionary
Anthropology in Leipzig, Germany. Prehistoric modern human burials, particularly those more recent than the time of the Neandertals, routinely include beads and red ochre, but “there is no patterning in this [Neandertal] stuff,” McPherron says."

[news.sciencemag.org]
"It's all about brains vs brawn and it took a while for Neanderthals to slip into a morphological niche they couldn't think their way out of."

[www.tested.com]
"For instance, only in Neanderthals, not AMHs, does body mass, and hence brain volume, increase over time."

Sorry, I have to stop adding to the list, I'm getting writer's cramps. Now if I only had the wrists of a (extinct for a reason dimwit) Neanderthal I could add a lot more.