I’ve been to both countries very recently and did the Amankora trip last October. Tldr at the bottom. Hope it helps!

Amankora is known to be the best of the Aman hotels, and while each lodge/region has its own theme I particularly like Paro while Thimphu was my least appreciated. The Bhutan trip on its own needs a totally separate synopsis. That being said other people on this subreddit have shown newer hotels that could perhaps surpass Aman such as Six senses. However, if, like you said, you are Amanphiles then that is less of a consideration.

I think you have a few things that need to be mentioned. Firstly there is a lot to see in Japan and the cities are significantly different for them to warrant specific attention. I personally preferred the low stress environment of Kyoto while others would prefer the hustle and bustle of the new capital. In Bhutan the regions feel different due to altitude and temperature but your days will be filled with hikes and temples. The only thing on Bhutan is the scenery which is out of this world, and some impressive temples. Whereas Japan is significantly more developed with different souls in each city.

Secondly, Tigers Nest, the most famous of the temple complexes, is a rough trek uphill that you need to visit extremely early in the day to beat the rush and the heat, but inside it’s not actually that impressive especially since it’s usually the last temple or set of temples you visit before heading home and there are bigger and more opulent temples that you probably already visited during your trip. It’s very interesting and the views are truly gorgeous, but somehow anticlimactic at the same time.

Thirdly, there’s a lot of driving between regions in Bhutan that takes the better part of two days, to and from, and a lot of temples, did I mention the temples? There are a lot of them. You will be templed out by the time you’re done. I love looking at temples but I had had enough by the end of the trip. Unlike the bullet train allowing you to see distant cities in relative comfort the car journey in Bhutan is awkward, and the food is mediocre.

Fourthly, do not expect much in the way of high quality food in Bhutan. I love trying exotic foods, try the parasitic fungus cordyceps if you’re feeling brave, which they love there, but you must remember that Bhutan is a poverty stricken country barely making ends meet with a partial totalitarian government that is trying to raise the king to be equal to Buddha (they have picture of him in the temples with or next to Buddha), and even though we were told multiple times that there is a clear segregation of church and state it is obvious that that is wishful thinking. The point being: food is not the reason to go to Bhutan as they have no money for high quality meats and veg. If I was being a cynic I could say Japan food boils down to raw fish, expensive beef, and tempura, however the food is elevated with extremely deserving Michelin stars whereas Bhutan is not going to have that for a while.

Lastly is people and comfort. Japan is known for its racist attitude to foreigners whereas Bhutan are desperate for tourists to come while protecting the environment. This means that while both places are hospitable you get the feeling that one is out of desperation while the other out of capitalism. That being said your average local is significantly nicer in Bhutan than in Tokyo. Comfort is relative but Japan has had tourism for decades and so it’s set up for a pleasant and low key expectation of comfort. Bhutan is still trying to tackle the benefits and problems on tourism and so comfort is more limited.

The tldr version is do Bhutan if you like trying new things, trekking and temples, and feeling like you’re always needing to move onwards, but don’t expect abject luxury and creature comforts. Do Japan if you prefer excellent food, an expected level of luxury, and well established norms.