정직하다 is an ethical term (honest) 솔직하다 is an emotional term (frank)

솔직하다: between being honest and being outspoken. 정직하다: between being honest and being truthful. 그는 정직한 사람이다: He never lies. He is upright and acts morally. 그는 솔직한 사람이다: He says whatever he feels (he has to), even if he knows that his words will upset other people or hurt himself.