It depends. Men and women's brains are wired differently. Did the switch alter the brain, or does it stay unaltered?
Assuming that the brain stayed unaltered, being a different sex for a certain amount of time would allow the hormones to affect the brain, so increased aggression or emotion depending on what state the mind is in.
With Billy/Carol, magic is also involved. Does the wisdom of a god stop the brain from responding to hormonal signals? Is Billy's body magically transformed into Ms. Marvel, or does an external body replace his, which he can use like an avatar?
Once all this is figured out, you'll get the answer if the sexuality changes.