Django-tastypie is no longer maintained by it's original creator and he created a new light weight framework of his own.
At present you should use django-rest-framework with django if you are willing to expose your API.
Large corporations are using it. django-rest-framework is a core member of django team and he get funding to maintain django-rest-framework.
django-rest-framework also have huge number of ever growing 3rd arty packages too which will help you build your API's more easily with less hassles.
Some part of drf will also be merged in django proper.
drf provide more better patterns and tools then django-tastypie.
In short it's well designed, well maintained, funded, provide huge 3rd party apps, trusted by large organisations, easier and less boilerplate etc over tastypie.
