Karate originated in Okinawa, Japan; Taekwondo developed in Korea. Both are striking arts, but their emphasis differs.
Karate distributes technique across hands and feet roughly evenly, with strong emphasis on stance, hip rotation and close-range power. Taekwondo places greater emphasis on kicking, particularly fast, high and spinning kicks.
For self-defence at close quarters, karate's hand techniques and low, stable stances are directly applicable. For athletic flexibility and dynamic kicking, taekwondo excels.
Traditional Shito-Ryu karate also carries an extensive kata syllabus and bunkai — the study of what each movement actually means in application.
Ultimately, consistency matters more than style. The art your child will still be practising in five years is the right one.