Hasn't the idea that homo sapiens were more intelligent been debunked in favour of the idea that they were more social and that's what gave them superiority
I don't know, but I suspect you mean compared to other hominids, while GP had non-hominids like chimpanzees and gorillas in mind, so I just wanted to make sure that that potential confusion is cleared up first.
No, see, this is exactly the type of misunderstanding I wanted to clear up: there is an entire lineage of different hominids that came after the split with chimpanzees. If we consider gorillas, orangutans and chimpanzees apes, then all of the hominids are apes. And all of those hominids either went fully extinct, or interbred with early homo sapiens to leave some living traces of their DNA with us, and then went extinct.
So "our predecessors" isn't specific enough. One might mean our pre-ape ancestors, like you do, or the subgroup of apes that is hominids.
Well, if they meant homo sapiens vs neanderthals, we have both skull sizes and genetic evidence suggesting that their brains were as capable as ours. We also have enough archeological sites of both early homo sapiens and neanderthals to have a decent understanding of the social structures we had. So it is possible to draw conclusions, even if it is never with 100% certainty.
Also, the debunking likely refers to the really old progressivist idea that any species that went extinct must have done so because it was inherently "inferior", instead of less well adapted to whatever changes the environment threw at them.
Either way, from what I understand the most recent well-supported theories of what caused neanderthal extinction is that their basal metabolic rate was so much higher compared to ours (due to adaptations to the ice age), that this simple caloric difference gave their body plan a long-term disadvantage over ours after the ice age ended[0].
And when I say "body plan" I refer to the part where apparently early humans and Neanderthals interbred so often that about 20% of Neanderthal DNA is still present in the modern human gene pool, and most humans have about 1 to 4% neanderthal DNA[1]. Similarly DNA from homo sapiens has also been found in neanderthal remains[2].
So were kind of reaching this point where Neanderthals and Denovisans seem to not quite match the definition that most people use when they say "different species". Our ancestors interbred a lot, and the genes that were advantageous stuck around. At that point using the word "extinction" without caveats becomes a bit misleading I think.