The main similarity is, that both dramas are about the life of a female student in an all-boys school.
When I started watching Professional Single, The male lead reminded me so much of Playful Kiss male lead. They both are cold and treated the female lead poorly at the beginning of their relationship. Also, the female leads' characters are kind of similar.
Both leads are childhood friends. The male lead liked the female lead first. Both female leads are strong-willed and work in the entertainment industry.