EDIT Outdated answer, tastypie is not really maintained anymore. Use Django REST framework if you have to choose a framework to do REST.
For an overview about the actual differences between both of them you should read their documentation. They are both more or less complete and quite mature.
I personally tend to tastypie though. It seems to be easier to set it up. It's done from the same people which created django-haystack which is awesome and according to django-packages it is used more than Django REST framework.
