If I am claiming my 19 year old child as a dependent but he has a child he is claiming as a dependent do we both file HOH?

My son is 19 and I am claiming him as a dependent for 2016. My son is also filing taxes and has a child he will be claiming as a dependent. I know when he files he needs to check that someone is claiming him as a dependent but does he also file as HOH? Should we file seperatly or would it be easier for me just to claim my grandchild as a dependent? (They both lived with me the whole year)