Actually the Neanderthal brain size was very comparable to today's modern Homo sapiens brain size and seem to average slightly larger than Homo sapiens sapiens.
Full brain endocast reconstructions of the Neandertals, Spy I and II, Djebel Ihroud I, and the Homo erectus specimen from Sal, Morocco have yielded accurate volumes. Spy I = 1,305 ml; Spy II = 1,553 ml; Djebel Ihroud I = 1,305 ml; Sal = 880 ml. While there are no remarkable gyral and sulcal patterns one can delineate, the brain endocasts do show evidence of left-occipital, right-frontal petalias, suggesting right-handedness, and possibly human cognitive specialization, involving symbol processing and visuospatial integration. Some speculations regarding Neandertal brain size are also offered, in which it is suggested that their possibly larger brain sizes were related to greater muscularity than in modern Homo sapiens.