Jem and Scout have a fairly typical sibling relationship of love and rivalry. Jem takes his role as older brother seriously, in both teasing and protecting Scout. For example, in Chapter 4, Jem learns Scout has eaten a piece of the gum left by Boo in the hollow of the tree:
When Jem came home he asked where I got such a wad. I told him I found it.
"Don't eat things you find, Scout."
"It wasn't on the ground, it was in a tree."
"Spit it out right now!...Don't you know your'e not supposed to even touch the trees over there? You'll get killed if you do! ... You go gargle right now...I'll tell Calpuria on you!"
Atticus and Alexandra have a much different relationship. Having grown up, the two have parted ways both physically and ideologically. Scout delineates their differences nicely in Chapter 13:
When Aunt Alexandra went to school, self-doubt could not be found in any textbook, so she knew not its meaning. She was never bored, and given the slightest chance she would exercise her royal prerogative: she would arrange, advice, caution, and warn.
How different this is than Atticus! Atticus taught the children to question everything. Unlike Alexandra, Atticus feels superior to no one, not even children. And while he too may "arrange, advi(s)e, caution, and warn," Atticus gives people free will, unlike his sister, who dictates from on high.
Jem is always protecting Scout when she eats food she found (like the gum in the beginninng) or with the Bob Ewell accident when he tried to kill them. He watches over her and tries to follow into his father's footsteps the best he can.