A diploid human cell contains about 6.5 billion base pairs of DNA. Each X-chromosome is about 0.16 billion base pairs, whereas the Y-chromosome is 0.06 billion base pairs. Therefore, female diploid human cells will contain about 1.5% more DNA than a male diploid human cell.
Note that in female human cells, the cells essentially crumple up and ignore one copy of their X-chromosomes, and only use one copy of their two X-chromosomes, so that extra DNA does not have major effects on cells aside from specifying the sex of the individual.
The Y chromosomes is not only smaller than X, but it has much fewer genes. At first sight most of the time but might not matter, because as was said half of the female X chromosomes are inactivated anyway.The problem for males is when one of the genes on an X is defective. That leads to both mild conditions like colourblindness and devastating ones like Lechs-Nyhan Syndrome and others (called X-linked diseases). The female with the same defective gene is OK because although one X chromosome is inactivated, it is not the same one in all cells i.e. half the cells will produce the normal gene product and that is usually sufficient for normal health and functioning.
Question said men and women but the same mechanism applies in placental mammals generally, but the story is different beyond that limited group.
I knew the answer. - I hoped @jerromyjon would take the time and thought to work with it a little. Guess not. Did you see the penguin post about the Adelie colonies on Danger Island? ...assuming your interest in your fellow Sphenisciformes.
I was starting with the premise that 4 legs is 1/3 more than 3 legs... but 3 times? Wow. Is that geometrically justified?
The Y chromosome is not Y-shaped, nor is a single copy of the X chromosome X-shaped. Below you can see an XY pair of a human male. You'll notice that the X chromosome is must larger than the Y chromosome. Note that if we count the X chromosome as being three 'units' in size and the Y as being one unit, an XX pair is 6 units in size while an XY pair is 4 units (~312 Mbp vs ~213 Mbp). So women have roughly 100 million more base-pairs than men.