Don't think that either is superior however, each is superior at specific things, obviously.
But here is some fodder for thought. Interesting Genetic Fact:
The female population currently outweighs the male population by 1% or so making the ratio 51% to 49% roughly. However, the male population is predicted to catch up and perhaps surpass the female population only slightly with modern medicine. Why? Because the sex chromosomes, XX for woman and XY for men, carry different genes. The X chromosomes carry large amounts of DNA information while the Y chromosome which is shorter than the X chromosome, only carries a few bits of genetic information such as the gene for becoming male. Essentially, we all start out female! It is the presence of the testis gene, called SRY, that determines the male gender.
Because the X chromosome carries large amounts of genetic information while the Y does not, males are more likely to suffer from disease and abnormalities than women. In genetics, two genes come together to determine a trait. One or both can be dominant or recessive. Disease genes are recessive as are abnormalities but if a male receives a recessive gene for a disease or abnormality, he is likely to express that gene given the lack of extra DNA information from the Y chromosome. Therefore, more male die in infancy than females. Does this make females genetically superior? Modern medicine will help combat early deaths from a genetic standpoint, helping even out the population. Let's not forget that females also develop faster overall, emotionally, physically, and intellectually.