Both places have their own culture, nature and food... Bhutan is still in my bucket list. I have been Sikkim and my experience there was amazing.
If you want, you can have a look to the below link to see some glimpse of sikkim beauty. https://www.youtube.com/playlist?list=PL-7au7SWuGMvI2vUUSZzyI9rH6IHJ1HVt