Ember is more of a fully featured framework than Backbone: it has bindings, computed properties and does some nice auto-updating stuff with handlebars templates — Backbone is more lightweight. Backbone is more popular and has been around for longer so it is arguably more battle-tested and there are more community resources.

Here's a podcast which contains lots of dialogue between the two framework creators (Katz and Ashkenas): http://javascriptjabber.com/004-jsj-backbone-js-with-jeremy-...