GP here, I agree with you, my characterizations were both pretty casual to the point of flippancy. I could write y’all a deeper essay on this stuff, but hey, I have LLMs to herd, the 17th century wasn’t my period anyway, and there is already a massive amount of insightful writing about these two thinkers to dive into.

I would say Hobbes in particular is a complex and difficult and frankly eccentric thinker; don’t make the mistake of believing you understand him; he is weird. If you really want to grok the guy in the context of his culture and historical moment, you should just read Quentin Skinner. That’s hardcore intellectual history though; for the basics I’d just go for the clear and brief and informative Oxford Hobbes: A Very Short Introduction.