The difference between Backbone and Angular is that AngularJS is more like Rails whereas Backbone would be more like Sinatra. What it means is , for complicated apps , you'll have to do complex stuffs anyway , so 'complicated' features are better built in the framework itself.
Unless you use a plugin , you'll have hard time updating your views automatically in Backbone if your model has nested objects. And your models cannot be arrays. In AngularJS it doesnt matter.
Backbone is not like Sinatra. Backbone is a hell of a lot more work than Sinatra. Backbone is a framework that more easily can fit atop existing design and services, however it takes so much time and in the end you just have even more complex spaghetti for someone else to maintain when you leave.
Unless you use a plugin , you'll have hard time updating your views automatically in Backbone if your model has nested objects. And your models cannot be arrays. In AngularJS it doesnt matter.