there's little difference in regard to nuiance
답변하다 seems closer to answering someone's question. mostly it is used for question
but. 대답하다 is different
you can use 대답하다 to answer someone's question but is unnatural to mean answering question. mostly it is used to mean react someone's call
when someone call you, you 대답하다 his call.
선생님은 학생의 질문에 답변했다.
james는 kim이 부르자 대답했다