Carnival does tend to get a bad rap. In my experience, there are two Carnivals: the short trips and the longer ones. It's those 3-day booze cruises that get the most attention. I have seen my fair share of those sailing out of Long Beach. That's where you would more likely see the fabled fist fights and vomit in the elevator. The longer cruises (7-10 days) tend to be more civilized. There will be fewer families with kids and more old folks like me. I actually prefer the food on Carnival over Princess. The decor will be more colorful, but decor isn't my number one concern.
Princess is not really "stuffy." The decor is more Versailles than Vegas, but the etiquette police are not following you around issuing sneers. If it's just the two of you looking for romance, Princess is probably the better bet. (I would choose HAL, but that's not the question you asked.) 🙂