You can only say '보고 싶다' as the meaning of 'to miss someone' (including pets, or animals). However, you can say '그리워하다' for someone or something (such as your childhood, hometown, good old days). e.g. 저는 언니가 보고 싶어요. (O) 저는 언니가 그리워요. (O) 저는 어린 시절 (childhood)이 보고 싶어요. (X) 저는 어린 시절이 그리워요. (O)

Salom

in general, same meaning both in using if say a little difference, " 그리워하다 " is meaning of mind and "보고싶어하다 " is meaning of action, but we can use as same meaning. hope you are happy with this :)