Why neither SSBNs nor SSNs are modern battleships

Is the SSN or SSBN the modern equivalent of a battleship?

Neither: the SSBN is a protected national deterrent, while the SSN is a covert ambush weapon rather than a visible instrument of naval presence.

An SSBN carries a national deterrent but contributes little to ordinary fleet operations; the navy must protect it and keep it away from the operational theatre. An SSN is a highly mobile ambush predator and war-fighting asset, but it lacks the visible presence function associated with a battleship. Strategic deterrence, fleet combat, and peacetime naval signalling are separate roles. Neither submarine type combines them in the way the battleship once did.