If Neanderthal had bigger brains (they did) or had different cognitive abilities, there's a chance they were baseline smarter than homo sapiens at the time.
Being perhaps a little smarter doesn't mean you win the evolutionary game. There are so many factors at play.
Considering most human groups have a % of Neanderthal DNA, they didn't exactly lose... Based on the % of Neanderthal vs. Sapien DNA, it seems Neanderthals were simply outnumbered.
<p><span><span><span><span><span>The Neumark-Nord discoveries are continuing to reshape our view of Neanderthal adaptability and survival strategies. They show that Neanderthals could plan ahead, process food efficiently and make sophisticated use of their environment.</span></span></span></span></span></p>
<p><span><span><span><span><span><span>The authors emphasise the sheer quantity of herbivores that Neanderthals must have routinely been ‘harvesting’ in this warm-temperate phase: beyond the remains of minimally 172 large mammals processed at that small site alone within a very short period, hundreds of herbivores, including straight-tusked elephants, were butchered around the Neumark-Nord 1 lake in the early Last Interglacial, within the excavated areas only. Other exposures in the wider area around Neumark-Nord have yielded more coarse-grained evidence of regular exploitation of the same range of prey animals, at sites such as Rabutz, Gröbern and <a href="https://www.pnas.org/doi/10.1073/pnas.2309427120">Taubach</a>. The last site contained cut-marked remains of 76 rhinos and 40 straight-tusked elephants. Roebroeks: ‘Safely assuming that with these sites we are only looking at the tip of the proverbial ice-berg of Neanderthal impact on herbivore populations, especially on slowly-reproducing taxa, could have been substantial during the Last Interglacial.’</span></span></span></span></span></span></p>
https://doi.org/10.1126/sciadv.adv1257
https://www.science.org/doi/pdf/10.1126/sciadv.adv1257 [PDF]
The text is in the article, second paragraph under "survival strategies". I don't see any obvious reason in the HTML why reader mode is skipping everything else.