I've worked on a reasonably large Backbone app in production and I've written several toy apps with Angular.
I think that a lot of people dismiss Angular as yet-another-mvc-framework without ever discovering the key elements of Angular that are actually novel and worthy of study. Personally, I think that Angular is a local maximum in client-side JavaScript app development. But even if you don't agree, you should at least understand how it is different.
1) Angular prefers declarative
This doesn't mean you don't write procedural code. This means that if you want to do something proceedural, you should package it up as a Directive. Directives are where behavior and logic live. Your templates simply arrange and parameterize a tree of directives. This means that you have limited and well understood moving parts that can be tested in isolation, in combination, or in the application context. Contrast with the traditional big bag of event callbacks, which can only be tested in the application context and are more difficult to re-use in other application contexts.
2) Angular works like a game engine
Most traditional UI frameworks are a graph of intertwined callbacks. Games, however, traditionally have a pair of functions called Update and Render. The Update functions permutes the world and the Render function draws the new world. Angular works similarly, but it might not be immediately obvious. There is a "Dirty Checking" pass, where your view models, a simple hierarchy of poorly-named "scopes" are essentially diff-ed against the previous iteration. Then the Directives take over and permute the DOM to match the new view model.
Let's call the "Controller" part of the "ViewModel" and then just simplify that down to "Model". Inherently, Model and View systems are co-dependent. You have a graph like M V. Angular's system graph is less like single bi-directional edge, and more like two directed edges in a cycle. That makes little difference when viewed abstractly with the two subsystems as nodes. However, once you break M and V down into subgraphs, the traditional Model & View systems look like a spaghetti mess of bi-directional relationships. An Angular application, on the other hand, would look like less like a lattice and more like a circle.