Max, as long as you are making an informed decision on seeing Neuschwanstein. For many people (Americans), its a must see because it is so well known in the US from the Disneyland connection. But there are also many people, including myself (three visits), who think less highly of it (its only about 70 years older than Disneyland), and especially when weighing the time it takes to get there, the long hike up the hill to the waiting area for your timed tour, the 20-30 minutes you are actually allowed in the castle, and the dejected walk down the hill. But that's me.
If your priority is mountain scenery, nature, nice alpine villages, hiking, etc., G-P is much more worth it, and other options like Mittenwald or Berchtesgaden, might more fit the bill. Munich is just not that close to the mountains. You use up a lot of time in just getting anywhere, and the time for a hike turns out to be not that much.