The larger brain size of the neanderthals though made them more cultured than modern man in terms of cave living, spirit and ancestral worshippers, they were, however, overridden by modern Homo sapiens and suddenly disappeared from evolutionary line.
The biological anthropologists believe that the overspecialization of the cranial capacity (brain size) and cold habitats of neanderthals were the cause of their extinction.
In short, this is just a matter of evolution. No real accurate reasons can be provided.
Hope this helps :-)