One of the symptoms related to PCOS is increased levels of male hormones.

What I am curious about is how this may affect a woman's personality. Would she tend to be more agressive, assertive, or dominate? Ugh, this probably sounds insane...

Insane? Nah! Sounds very bright to me! Actually, it can make you more aggressive and have a shorter temper if the levels are high enough, but if they are only a little high, most women just complain about altered sexual desire and depression. For me, it depends on the day!

Higher testosterone usually means a HIGHER sex drive.