Read ZUNs afterward on Wiki about Touhou 12. It gives quite interesting information.
While the Extra theme fanboys love it. I don't love it. But neither I call it bad and "LOL THIS SUCKS". It is just not giving any charming effect. Same goes for Stage 4 bgm, also not charming.
Personal feelings about music:
Stage 1 - Awesome opener, pumps you up for the game. Very energetic and "flying"
Nazrin - Fits. Have no complaints. You can literally hear the mouse play.
Stage 2 - Again good follow up stage song. You feel like going even higher into the sky chasing that ship.
Kogasa - Fits. The poor umbrella's song is brought to life. At the raincard spell it fits even more as the music synchs great.
Stage 3 - I feel like being close to that ship in the sky. Yet you can't reach it yet.
Ichirin - Opening is really poor but it becomes better through out the song. Not charmed.
Stage 4 - Unexpected change of tune and style. Fits the "wtf is this ship no treasure" theme. Groovy and dark.
Murasa - The best opener in the entire game for my feeling. It really pumps you up for the battle. Just like Kogasa's theme.
Stage 5 - You know you are somewhere weird and it feels grand. Nazrin appearing here also fits the theme again.
Shou - Unexpected boss song, sounds sinister but I am really not charmed. The song and her appearance make me thing of ancient Aztec.
Stage 6 - Heart fills up the void. It is quite dramatic as if you can hear the heart of Byakuren beating. Though it is not pumping you up for battle, it does gives that dramatic feeling. Especially when suddenly seeing Byakuren's beauty (she is drawn within a gloomy/dreamy haze imo).
Byakuren - Cosmic Mind for sure. It fits the character, her desires and motives. It fits as a final boss to me. It caused me goosebumps which I only had with Kanako's theme and Remilia's theme in Touhou.
Extra stage - It feels very unspired but somewhat fitting. I can't really judge this song. It just is not complete.
Nue - I guess it fits her weird unpredictable form and appearance. But aside from that it is not a charming song. I don't care if it reminds people of U.N Owen. If you discard that, what is left over is uninspired.
To sum it up:
Stage 1, 2, 3, 5 and Nazrin, Kogasa, Murasa, Byakuren are the ones that on first hearing caught my attention. Doesn't mean I hate the other songs.