There are hypotheses that Neanderthals were actually smarter than our other ancestors, and that they were wiped out for various reasons unrelated to intelligence. They may have been less violent than homo sapiens or seriously weakened by pathogens that didn't affect homo sapiens.
Or simply less numerous. We do know that many of us (Europeans and Asians) have some Neanderthal DNA, it's entirely possible they were just bred out of existence.
However, a smaller brain might have been better at that time. For example, a bigger brain requires more energy.
On the other hand, death in childbirth was a major hazard for females. Although I think Neanderthals' brain size at childbirth was similar to that of modern-day babies - but later it grew faster.
One has to wonder: if there were ever any other intelligent species (that we couldn't breed with) on this planet alongside us, then we probably wiped them out..
Why would we necessarily be what wiped them out? Intelligent dinosaurs may have been wiped out by an asteroid/volcanic activity/climate disruption (or whatever the most current theory is).
While they werent dumb lizards, i havent heard anyone claim dinos were dolphin or ape-smart. The brains were small and structured very differently than animals we today consider smart.
There are hypotheses that Neanderthals were actually smarter than our other ancestors, and that they were wiped out for various reasons unrelated to intelligence. They may have been less violent than homo sapiens or seriously weakened by pathogens that didn't affect homo sapiens.