We've seen a number of departures from TOS to TNG. There is a lot that is dissimilar. The fact that Klingons and Romulans are depicted differently comes as no surprise. Is it glaringly so? I'm not so sure with the Romulans, as we get only 2 episodes of them in TOS. They are highly militant and almost like Roman soldiers in terms of strict military code. But yes, a son of a Senator will carry weight more than a son of a pauper. That's true even in the real modern world we live in.
"Balance of Terror" established the notion that the traditions of honor that the Commander and Centurion valued were considered out of date in the Empire and had given way to a younger, more self-serving generation. So there's canonical support for the idea of Romulan culture changing and moving away from its traditions of honor. So that transition never really bothered me.
Really, it shouldn't be surprising at all if a culture's values change from one century to the next. An American from 100 years ago wouldn't have recognized modern American values: a black president, women in positions of authority, gay marriage starting to be legalized, America as a global power rather than tending to its own affairs, etc. What would be implausible is if a culture were exactly the same in the 24th century as it had been in the 23rd or 22nd.