It may not be the largest castle in Europe, but...
(Taking a linguistic/cultural detour here...)
It may not be a castle at all (and the same applies to its neighbor, Hohenschwangau) to Europeans. It is only the English-language's lack of precision when it comes to this type of building that we now refer to it as a "castle."
The Germans (and Neuschwanstein IS in Germany, after all!) as well as the Austrians and the Swiss refer to N'stein as Schloß Neuschwanstein, and Schloß, if you are curious, is German for "palace."
Schloß is not to be confused with their word for a real castle, ( which is Burg) and which refers to a building from the Middle Ages that was constructed for the main purpose of defense from invaders. Think thick heavy walls, turrets, bows and arrows, catapults, maybe boiling oil, etc.
A Burg was not designed for living in the kind of luxury that Bavarian King Ludwig II came to expect in the late 19th century (around the same time when skyscrapers were going up in Chicago,) so German speakers would never refer to N'stein as a Burg. It is a Schloß, hands down.
When they say "Schloß", they mean what we think of as a palace. When they say "Burg" they mean traditional medieval castle (or ruined castle.)
The only time Germans can't decide which word is right is when a palace has been built on top of Burg, which has taken place here and there, but there is no confusion at all about Neuschwanstein, which despite its fake castle facade, is a Schloß for sure.
Always good to know what you are actually seeing, I think, and to know how the locals see such things as well.