I am lucky enough to have both a boy and a girl. I've noticed some major differences in their behaviors, especially how they resolve problems. Let me describe further.
Toddler Girl Response: A toddler girl will whine and complain uttering the word they use for food repeatedly until someone gets annoyed enough to get them what they want.
Toddler Boy Response: A toddler boy would simply find some dirt, toy or pencil to chew on until their hunger passes.
Problem: A Boo-boo
Toddler Girl Response: A high pitched scream amongst the normal crying for added dramatic effect. The toddler girl must make sure everyone nearby can hear and feel her pain.
Toddler Boy Response: Lower the bottom lip and run directly to mommy because only she can make it better.
Problem: A toy or food up high out of reach
Toddler Girl Solution: Scream, whine, throw herself on the floor until someone gets her what she wants. She'll demand an immediate response right away.
Toddler Boy Solution: He'll crawl up onto the garbage can, up onto the counter, across the sink, and get the item himself.
Problem: A dirty diaper
Toddler Girl Response: She'll find an adult and point to her rear screaming and muttering disgustedly. She'll insist they change her at once.
Toddler Boy Response: He'll continue playing - this isn't a problem.
Problem: A broken toy
Toddler Girl Response: She'll insist daddy buys her another one immediately. She'll act as though it was the only toy in the world even if she never played with it.
Toddler Boy Response: Dismantle toy further since it's already broken.
Problem: Clean up time
Toddler Girl Solution: Girls will pretend to be asleep. If that fails, whine, move incredibly slow and make parts of her body go limp while being forced to clean.
Toddler Boy Solution: A boy will throw toys as hard as he can into appropriate boxes and bins all while wearing a little evil smile.
Of course this isn't true for every little boy and girl. I'm sure there are some overly dramatic boys and some daring little girls out there. These are just some of the strange little differences I've noticed in my own household between boys and girls.