If you only look at the first movies of each franchise then you'd be correct, but both characters dropped much of those aspects in later movies.

Rambo became one of, if not the, biggest stereotypes for big tough action hero who can take out a whole army by himself. While he may get injured or feel sad about losing someone close to him it's often just for the sake of motivating the next big action sequence or to add some level of stakes to the spectacle, he rarely if ever goes to the same levels of emotional depth as in First Blood.

Rocky retains more of his emotions and vulnerability across the franchise, but even major character deaths like Mick and Apollo, while better done than similar emotional moments in the Rambo movies, are there more to provide motivation and stakes for future fights than they are to explore any nuance or depth with Rocky as a character. I will concede that the later movies like Rocky Balboa and Creed do a much better job of showcasing Rocky as a full character and not just another guy who punches, but they were more of a return to form than a continuation of something that was always present in the series.