Day trip from Munich to Neuschwanstein

My wife are going to Germany in late August and wanted to visit Schloss Neuschwanstein and Hohenschwangau. We were planning on doing this as a day trip from Munich instead of staying in Füssen, but we're wondering if we should attempt to do this on our own or as part of an organized tour.

My understanding is that the castle tours are pretty regimented, so it's not like we can get much additional time there by going by ourselves, and the tours seem relatively inexpensive (the one I'm looking at is 90 euros per person, which includes the castle tour, train fare, and a tour guide, and free time in the area to allow you to visit Marienbrücke).

When I look at the train fare from Munich to Füssen alone it appears we'll be paying around 100 euros, so adding in transportation to the castle itself and entry, it seems like a no-brainer that the tour is a better option and I'm just curious if I'm missing something.

Any advice on how we should manage this trip would be appreciated!