I used Falcon for a relatively large project and enjoyed using it. It is noticeably faster than Flask and I can write code faster as well. It is very much still growing and features are being added. They call Flask "Batteries not included" but Falcon takes that to another level. There are also not very many extensions in comparison to Flask. If you are writing an API exclusively, I would choose Falcon. However, if you have any HTML/CSS/JS, Falcon is probably not suited for the project.

EDIT: Both are very good.

For just simple API stuff, CherryPy is another good option.