Well they hard larger brains, more muscle mass, larger sinuses which aid in breathing in cold weather and possibly smell, denser bone structure, and a number of other possible advantages.
It has been proposed that the advantage we wield which led to out-competing / interbreeding with them may have been a superior ability to starve - i.e. use fewer calories - during periods like the last ice age.
"Neanderthals appear to have matured faster physically but had a slower reproductive tempo overall, with longer spacing between births. That suggests fewer offspring over a female's reproductive lifetime."
So my theory is that they could well have been more sophisticated in a lot of ways, but were just outbred.
Ive also read some out of wack theories like some conditions like autism could come from them since its more prevalent on white people. This would explain that a group that engages more socially creating bonds and more complex societal tribes in number would outnumber and extinguish these weird less verbal humans
It's far from conclusive, not representative of the majority of folks with autism diagnoses, and needs more replication and investigation. But it could be a thing. Speaking as a spectrum-y red-haired middle-european.
It has been proposed that the advantage we wield which led to out-competing / interbreeding with them may have been a superior ability to starve - i.e. use fewer calories - during periods like the last ice age.