The TVTropes Trope Finder is where you can come to ask questions like "Do we have this one?" and "What's the trope about...?" Trying to rediscover a long lost show or other medium but need a little help? Head to Media Finder and try your luck there. Want to propose a new trope? You should be over at You Know, That Thing Where.
From your statement "That was probably a decent restaurant, but since it's a franchise of [Fancy Restaurant Chain] it just suffers from Godfather 3 Syndrome..." It sounds like Unpleasable Fanbase or any other kind of Fan Dumb.
MAX POWER KILL JEEEEEEEEWWWWWIt's similar to Sequelitis, but it's not that the movie was "worse than the original", it's that it's a decent film, just not worthy of the franchise. If it'd never been connected to the franchise at all, people would be loving it. It's like the extreme opposite of Better by a Different Name: It's "Better if it had never been known by any name at all" :)
I just read the description for Contested Sequel, and that seems to come closest.
My wifey and I have a name for sequels that are BAD, but would have been adequate, or even GOOD if it weren't connected to the obviously superior previous installments. We call it "Godfather 3 Syndrome".
Many people agree that the Godfather Part III was the worst of the sequels. Some even go so far as to pronounce it so bad it's horrible. But most people I speak to agree that the film would have actually made a decent movie if it were just a random Mafia flick about an retired Don attempting to go straight. If the lead wasn't actually Al Pacino, playing Michael Corleone, it would have been a great movie. But it suffered by comparison.
Is there a trope for this? My lovely spouse and I use this term now to apply to everything. "That was probably a decent restaurant, but since it's a franchise of [Fancy Restaurant Chain] it just suffers from Godfather 3 Syndrome...". "That would have been a better show if it wasn't an Aaron Sorkin project. I guess I just expected better". It's LIKE Sequelitis, except that the sequel is actually GOOD, just not as good as what's come before.
I'd add it to YKTTW, but I'm not sure if Godfather 3 Syndrome is a clear name for it. Or what you'd even call it if not Godfather 3 Syndrome. [shrugs]
Edited by Draconius