The whole design of DRF makes a lot more sense for my use cases.
TastyPie provides you with Resources that do everything from accepting and dispatching methods, querying db, authentication and authorization to parsing an serializing data. If you want to modify one puzzle you have to redefine the resource.
In DRF the separation between request processing, data serialization/deserialization, rendering and other elements is more clear.
API endpoints are just views that are based on Django class-based views so you should already know how to customize them, do queries and use mixins. Serializers perform data validation (similar to forms, but can handle collections and relations) and conversion between objects and native Python datatypes. They can also be reused in multiple views or for nested relations. Other components are pluggable so you can specify parsers, renderers and auth backends for the whole API or for just a particular view.
The Rest Framework just feels right and works well when you need to do any sort of customization. On top of that you get a very detailed documentation and a browsable API.
TastyPie served me well for a long time and I'm very thankful to the developers, but I find DRF to better suit my needs.