Django REST framework is a powerful and flexible toolkit for building Web APIs.
Some reasons you might want to use REST framework:
The Web browsable API is a huge usability win for your developers.
Authentication policies including packages for OAuth1a and OAuth2.
Serialization that supports both ORM and non-ORM data sources.
Customizable all the way down - just use regular function-based views if you don't need the more powerful features.
Extensive documentation, and great community support.
Used and trusted by large companies such as Mozilla and Eventbrite.
flask-restful-swagger is a wrapper for flask-restful which enables swagger support.
In essense, you just need to wrap the Api instance and add a few python decorators to get full swagger support.
Flask API is an implementation of the same web browsable APIs that Django REST framework provides.
It gives you properly content negotiated responses and smart request parsing.
It is currently a work in progress, but the fundamentals are in place and you can already start building kick-ass browsable Web APIs with it. If you want to start using Flask API right now go ahead and do so, but be sure to follow the release notes of new versions carefully.