I recently re-watched Holy Grail and followed it up with Life of Brian, and I noticed that while both are funny, they're funny in very different ways.
Holy Grail is mostly a light-hearted parody of Arthurian legend. They took the framework of the quest for the Holy Grail, and injected it with the kind of surreal humor they're best remembered for. The closest thing to social satire in it is the oft-quoted scene where Arthur and the peasant argue over how he came to power, and that's more funny because it's totally absurd than because it's making any kind of statement.
Life of Brian, on the other hand, is very heavy on biting social satire. It's critical of beaurocracy and religion, chiefly. Most of the humor comes from mocking the people's way of being more concerned with being followers of the messiah than listening to the messiah's message, the way the Judean People's Front is a committee mired in bylaws, not really acting, most frequently infighting with the JPF, PFJ, Judean Populist Front, et al. The scenes you quote "It says 'Romans Go Home'" "No it doesn't!" are exceptions to the rule for Life of Brian.