The Empathizing-Systemizing (E-S) theory of typical sex differences suggests that individuals may be classified based on empathy and systemizing. An extension of the E-S theory, the Extreme Male Brain (EMB) theory suggests that autistic people on average have a shift towards a more masculinized brain along the E-S dimensions. Both theories have been investigated in small sample sizes, limiting their generalizability. Here we leverage two large datasets (discovery n = 671,606, including 36,648 autistic individuals primarily; and validation n = 14,354, including 226 autistic individuals) to investigate 10 predictions of the E-S and the EMB theories. In the discovery dataset, typical females on average showed higher scores on short forms of the Empathy Quotient (EQ) and Sensory Perception Quotient (SPQ), and typical males on average showed higher scores on short forms of the Autism Spectrum Quotient (AQ) and Systemizing Quotient (SQ). Typical sex differences in these measures were attenuated in autistic individuals. Analysis of "brain types" revealed that typical females on average were more likely to be Type E (EQ > SQ) or Extreme Type E and that typical males on average were more likely to be Type S (SQ > EQ) or Extreme Type S. In both datasets, autistic individuals, regardless of their reported sex, on average were "masculinized." Finally, we demonstrate that D-scores (difference between EQ and SQ) account for 19 times more of the variance in autistic traits (43%) than do other demographic variables including sex. Our results provide robust evidence in support of both the E-S and EMB theories.