100% they were more advanced than early homosapiens. In fact I will argue that they are what made humans human. I went digging through their dna last year and Altai, Vi3315, and Vi3319 have the CYP21A2 rs6467 (C;T) variant
Their DNA is up online, but you can also see these variants here: https://academic.oup.com/humrep/article/36/3/734/6071469
They were highly inbred and they were carriers for this form of Congenital Adrenal Hyperplasia (CAH) due to 21-Hydroxylase Deficiency. Even in its nonclassic form, this would have contributed to the low population numbers as any classic form would have been non-viable as well as resulted in evolutionary pressure to select for the genetic variants to compensate for the altered HPA-Axis. Neanderthals are most known for contributing to human specific DNA sets such as improved immune system, but if you go digging you will notice the larger pattern.
NCAH specifically results in higher neurogenesis. They were smarter. They also now had a bigger glucose preference and started to shift calories to grain. At some point between 130-70KYA there was enough excess calories from grain to not need to eat the dead. (see their teeth between this time) Admixture with modern humans occurs around 50-43KYA. These adaptations would have contributed to the loss of the mitochondrial DNA due to low female reproductive success compared to the higher male Neanderthal with female human success. The 2-4% that is found together is found together for a reason. They are incredibly valuable together.
This support for reduced HPA-Axis would have allowed for many other variants on the HPA axis and while not a single genetic variant, atypical HPA axis phenotype is associated with intelligence due to the enhancement in ability to detect unexpected events.
The glucose/grain preference with higher caloric density supported the higher population densities that occurred rapidly due to the Younger Dryas (last glacial period) and resulting agricultural and villages transition in Mesopotamia. These agricultural populations outcompeted other human groups while spreading the Neanderthal derived genetic variation.
