I'd argue this is too expansive of a view. It's a debate specifically coming out of the English Civil War, and specifically focusing on the tension between Parliament and the Monarchy. If you read Clarendon it becomes extremely obvious. Hobbes (like Clarendon) took the royalist view defending the king, and Locke set for an argument for parliament.

Some of it doesn't translate super well into modern times. For example, Locke barely touches upon judiciary. The modern notion of separation of powers came (I believe) from Montesquieu.

I will say that Hobbes gives a far more comprehensive argument than Locke does. And some of Locke's details, including his anthropology of the origin of commonwealths, is demonstrably false.

Either way, glad to see Leviathan here!