I see one significant advantage from the FamilySearch map search function: It recognizes some historical place names that Google Maps doesn't know about. My best example of this: I tried searching for "Wiltwyck, New Netherland" and FamilySearch showed me a map that correctly associates the historical name Wiltwyck with modern-day Kingston, New York, and associates New Netherland with the Hudson River. In contrast, Google Maps cannot find New Netherland, but it does find some local features in Kingston that use the "Wiltwyck" name.
However, the FamilySearch label for Wiltwyck makes me cringe -- "Wiltwyck, Ulster, New York, British Colonial America." Wiltwyck was a Dutch name that wasn't in use under British control, when names like Ulster County and New York were applied. And FamilySearch fails when I try the Dutch spelling "Wiltwijck."
One advantage of Google Maps Search over FamilySearch is related to map scale. In modern searches Google often takes me to a map scale that is appropriate for the scale of the feature I was looking for (I get a smaller-scale map when I search for a state than when I'm searching for a neighborhood), while Family Search consistently serves up a very large-scale (hyperlocal) map for a modern name and a very small-scale map for a historical name.