We stayed in Amankora Bumthang and it was a wonderful experience, one that we will never forget. We were in Bhutan for 11 nights, started in Thimphu drove to Bumthang and went back to Paro.
The trip between Thimphu and Bumthang is what is recomended if you have 10-11 days.You can do this trip and stay in all Aman lodges if you want. There is a very lovely hotel in Paro called Uma that is not as expensive as Amankora but it is as good, and other that these two there are not any luxury hotels but there are some nice ones that could give you a very memorable experience. Bhutan is a very special place with special people.

I would recommend mixing it up by staying in at least one or two local hotels. IMO an all Aman trip would insulate you from a more local experience. The Olathang Hoel in Parao is quite a nice local experience. Bumthang doesn't have a lot of choice places so an Aman there would make sense.
When I was there in '07, some local people expressed unhappiness with Aman; apparently they had promised more jobs for locals and other community perks (in exchange for building privileges) that have fallen short of expectations.
Even if you stay at Amans, you can elect to get your own guide I believe. There are agencies in Bhutan who could find you a photography guide (one who knows what time of day to arrive at a location, best viewing site, etc)

We spent three weeks in Bhutan last autumn. No way would we have used establishments like Amankora. As Robbietravels points out their promises have failed to deliver and we personally feel that these upmarket chains are not ecologically sound. Apart from the exorbitant prices they charge the question perhaps has to be asked why go to Bhutan and insulate yourself from the country and its people by stopping in places like this rather than other tourist hotels? The standard of hotels we stopped in was perfectly acceptable, although once in the east of the country standards were more basic, and in the far east very basic.

On the more general question of location and scenery we would probably say that the west (Paro and Haa), Phobjika and Bumthang were the areas we liked best.