The mammoth traps in question are from about 15,000 years ago. Neanderthals went extinct something like 40,000 years ago.
Neanderthals were more ancient to the people that made these traps than the traps are to us. (Also, I'm unaware of any evidence of Neanderthals in the Americas.)
Neanderthals had larger brain cases which suggests they had larger brains, though it's not understood why their brains would be larger -- what evolutionary advantage did it confer? Why wouldn't Homo Sapiens have a similar volume of brain case?
One speculative theory is that Neanderthals, with apparently better night vision and sense of smell (based on size of ocular orbits & nasal passages), had larger optic & olfactory centers in their brains. This seems a tenuous argument, however.
If brain size is directly proportional to number of neurons and neural links, then Neanderthal brains (and the larger brains of certain other mammals) would be more complex than ours, have more capacity, more memory, or other capabilities.
It's not clear why a mammoth or other elephant-like creature would have such large brain (the African elephant's brain is about 3 times as large as a human's). Perhaps there's some redundancy in the tissue, or legacy regions that are not used today.
Elephants are remarkably intelligent, and one can assume similarly the mammoths. Elephants have a sophisticated culture and have been observed to do a dance to welcome another elephant returned from a trip. They do have excellent memory; the saying "elephants never forget" seems to be true. They remember watering holes all over the savannah including ones that no longer exist on the surface, and they know to dig down and find the subterranean water in the exact spot that they hadn't been to for years. Social interaction is also important for brain development. So who knows? Maybe there's more to pachyderm intelligence than we are currently aware.
>It's not clear why a mammoth or other elephant-like creature would have such large brain (the African elephant's brain is about 3 times as large as a human's). Perhaps there's some redundancy in the tissue, or legacy regions that are not used today.
This, at least, I can answer, using numbers from https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4053853/ . The elephant brain is massive, but 97%+ of those neurons are in the cerebellum, and is likely related to their somewhat unique use of a trunk. And while their cerebral cortex is twice as massive as a humans', it only contains one-third the neurons.
Neanderthals were more ancient to the people that made these traps than the traps are to us. (Also, I'm unaware of any evidence of Neanderthals in the Americas.)