From what I hear most fans seem to be rather satisfied. They probably would have been upset if it was radically different since what the fans always wanted was another Shenmue game after 18 years. If they can make a Shenmue 4 than maybe that game they would want to try to make more different.
As for Final Fantasy 7 it looks like they aren't just banking on nostalgia and living in the past, the whole structure of the game is completely different, different combat system, new voice actors instead of using the compilation actors, updated designs for the characters, scenes and levels being expanded, slightly altered and new stuff being added on as we've seen, making Midgar into a full game, of course though it still has it's large amounts of nostalgia obviously since at the end of the day its a remake. But at the same time thats whats making some people iffy on the remake since all they wanted was the exact same game but with better graphics.
Either way its hard to compare since FF7 is a remake and Shenmue III is a sequel.