From the three castles, all built (or let's say, tried to be) by King Ludwig II, I have only visited Neuschwanstein and Linderhof. Herrenchiemsee sounds like a great third site but is just far away from the other three so I couldn't fit it into a trip and unsure if I ever will. There is also an unsung fourth site called the King's House on Schachen which is a hunting lodge in the Alps and not easily visited, but also not that exciting from the looks of it. I would think that whenever inscribed it's probably not included.
Neuschwanstein, on the Romantic Road, is a highlight for many, many tourists. It doesn't need world heritage status and already has packed tours every 5-10 minutes in multiple languages, with hordes of Japanese and Chinese tourists making up many of them. It also gotten so bad that heaps of tax exempt shops have cropped up around the village below catering these crowds. Nonetheless the castle itself is a masterpiece. The exterior seems complete but inside you only get a few rooms and one large hall that have been completed. It's unclear how the builders worked back in the days because when you build a house now you don't decorate it room by room, do you? Anyhow, everything besides those rooms is just grey walls or used by the staff including the souvenir shop. The rooms that are complete are masterpieces though, showing Ludwig's love for Richard Wagner.
Linderhof is much smaller and as you can see in my picture was unfortunately under renovations during my visit but still open for tourists. It's a typical manor though, not as grandiose as Neuschwanstein or the site at Herrenchiemsee. It's main draw is also the park I think rather than small building.
If you are not familiar with the history, King Ludwig II pretty much spent all the money of the state on building these and ran out of money, died young, and left a huge debt behind. He still seems to be highly regarded due the legendary buildings left behind, and maybe actually making the state money with all the tourist dollars/Euros it brings it now. Go Ludwig!