Personality-wise, Emma is a person of a calm demeanor, which accurately denotes her inner state of mind. The girl has always been difficult to faze, rile up, or get any kind of extreme emotional reaction from. Ironically, this distinction, which often causes peers to regard such a person with certain respect, has constantly caused her trouble in social interaction due to its persistence. It's not that she is more mature than others her age, or more in control of herself - she just plain does not feel as much, cannot care as much as other people. As such, instead of being revered as the mature older sister type, she would be considered just distant, unfriendly, hollow, and later on, when the kids learned more crass language and cruelty, "a frigid bitch", "inhuman" and the like.
That namecalling does not actually reflect her character, at all - if anything, her decreased sensitivity has led to her caring more than the average person. Emma is a person of strong morals who won't hesitate to extend a helping hand to someone who needs it, even if doing so puts her into danger - she may not be able to feel for them in most situations, but that should not stop her from doing something for them. Even if "they" are jerks - it's not like she really cares either way for their behaviour.
On a different but very much related note, in retrospect, polite honesty may not be a good combination with a lack of ability to distinguish the sensitivity of one's words and actions. But while she has been reconsidering that stance as of late, old habits die hard, and so, for the time being Emma remains her usual self, often coming off as unpleasantly blunt, if not outright offensive, by saying something that, while entirely true, should have been left unsaid.
In all honesty, Emma is rather mystified by the way other people can get worked up over meaningless things, maybe even a bit envious of the high tension and excitement she so often sees but so rarely feels. This may be another reason for her choosing to work for TSAB as well as for her choice of fighting style - in the midst of combat, the world rushes by at an unnaturally slow pace, and despite the contradiction, she cannot find better words to describe the feeling; everything is brighter, more vibrant, fuller of life, of magic, of feeling, including herself. On some level, Emma realizes that this may not be a healthy direction to head into, but that realization is not yet truly formed into something that can guide her actions and decisions.