Is it worth it to remove an old cherry oak tree?

[Jason L.]

I have an old cherry oak tree on one of my properties where one of the branches fell off last week. There wasn't a storm or anything. As far as the tenant knows, the branch just kind of fell naturally. I could have the whole tree removed for $500 more than just removing the debris, but I don't know anything about trees to know if that's actually worth it (even the tree contractor I want to use said he didn't think it was 100% necessary). Has anybody dealt with cherry oaks or any type of tree-related problems before?