Personally, I don't think it's a girl thing or a boy thing...it's an individual kid/person thing. Our son is such an incredibly sensitive child at times, it baffles me. Some of it I can understand, based on various disappointments, and some is totally just him from day one. He's 12 and he still surprises me with his emotions at times.
Sometimes I just want to say, "Get over it!" But how much of that is my expectation of what I think a healthy child should be or do, and how much of that is my frustration over having an emotionally needy child?
It's not uncommon for twins to be totally different. My husband and his twin brother couldn't be more different from each other--when they were kids and at their current ages of 55. All along, they've barely looked like they're in the same family. They went to different high schools because of totally different interests and abilities. One knew what he wanted to be when he grew up since he was a kid (mechanic/fireman...eventually became fire chief); the other has done several totally different things throughout his life. One was the instigator and the other was the follower. One is half bald with broad shoulders and the other has a full head of hair and is skinny as a rail. The list is endless, personality-wise and looks-wise. (They both have similarly stupid humor but that's more a learned trait than anything. : P)
My husband's cousin's twins (boy/girl) are quite different as well. The girl is the forward and confident one; the boy is the more shy one. So, it depends more on the genetic makeup of each individual child.
I truly believe personality is part of the hard-wiring from the start. What we do with the hard-wiring can emphasize or counteract some of those traits. But some of it is just who the child is.
My only caution is to let each child be their own person. I've always been impressed with how my in-laws seemed to allow the twins to develop into their own individual strengths. But be aware that twins often take different roles, some because of who they are and some because of the other one doing it for them.
Sometimes, parents can unwittingly perpetuate those differences. For instance, it's not so noticeable now, but when my husband and I first got married, there were two things I would see my husband and his brother bristle about. My husband was the "brain" and his twin was "Mr. Fixit". One felt inadequate when it came to fixing things, the other felt inadequate when it came to "brainy concepts". Since that time, my husband has gained much confidence with regard to fixing things (owning a home for 14 years has a way of doing that to some people). His brother has gotten his bachelors degree and has much more confidence regarding his academic abilities. Those were some deep-seated feelings that the parents helped perpetuate, unbeknownst to them.
Your twins are still very young, so be careful of labels. It almost sounds like you expect your boy to be active and a "monster" and you expect your girl to be a "princess". That's not totally true because you seem non-plussed by her behavior. Yet, could it be that she is just a hungry girl and is growing differently than her brother?
My husband's cousin's twins are a case in point. The girl has always been bigger/taller than the boy and has often has a more voracious appetite. She's not fat, she has just consistently been taller than her brother, sometimes by as much as 6 inches! They are now 13 and he is beginning catch up but they are definitely different with different needs and wants.
My best advice I can think of is to give support, comfort, and guidance as needed. And celebrate their differences and respect their needs.