The main difference between Scout and Jem is their ages and respective maturity levels. Jem is older and generally more aware of what is going on. However, both children are equally compassionate and intelligent. They are aware of the world around them and reflective of it.
Since Jem is older he often bosses Scout around. Even though she does not like it, she usually listens to him.
Dill blushed and Jem told me to hush, a sure sign that Dill had been studied and found acceptable. (ch 5)
Jem often scolds Scout for acting like a girl (even though she is one) because he considers her more of an equal when she is acting like a tomboy. Jem also protects Scout (and she is protective of him too), such as in the courtroom when the discussion of rape made the reverend tell them to leave.
Jem scowled furiously at me, then said to Reverend Sykes, "I think it's okay, Reverend, she doesn't understand it."
I was mortally offended. "I most certainly do, I c'n understand anything you can." (ch 17, p. 123)
Jem is being mature, protecting his sister. However, he also wants to stay to see the trial. He seems to understand more of the trial than Scout, although she understands quite a bit for a nine year old.
Jem and Scout are both morally upright children who enjoy growing up in Maycomb, Alabama. Both siblings appreciate the outdoors and participating in physical activities. Jem and Scout are both intelligent, curious kids throughout the novel. They are continually experiencing new things together and support one another. They share the same friend, Dill, and both look to their father for advice.
However, their age difference and expected gender roles set them apart. Jem, being four years older than Scout, often understands situations at a deeper level than his younger sister. Jem also attempts to boss Scout around and distances himself from her as he begins to hit puberty. In contrast, Scout is naive and looks up to her older brother. She approaches Jem for advice and thinks highly of him. Scout cannot participate in many activities that Jem is interested in, like football, but continues to support his dreams.