Jo and Laurie are alike in terms of the way neither one really embodies the qualities typically associated with their own gender. Jo is bookish and headstrong; she hates getting dressed up, and she envies the men who go away to the war as well as Laurie when he gets to go away to school. She is quite prideful rather than submissive, even refusing to ask Aunt March for money when Marmee needs it. Instead, she sells her own hair, wearing it short (like a boy's) until it grows out again.
Laurie prefers music to study; he is sentimental and romantic. Jo is more logical than Laurie, another apparent gender reversal. For example, Jo tries to subtly prevent Laurie from proposing to her, and then, when he does, she rebuffs him. Society would dictate that Jo, a girl from a poor family, ought to jump at Laurie's offer, that she should be not only grateful but also wildly in love with him, the handsome well-to-do family friend who is so solicitous of her happiness. Then, she goes far from home to strike out on her own and become a published author (also a profession usually associated with men at that time). Even their nicknames are gender-swapped: Jo is typically a boy's nickname, and Laurie is typically a girl's.