I see that you shortlisted only 2 frameworks/libs (AngularJS and ReactJS) but there are quite a few choices. My choice and recommendation is VueJS. I think Vue has very simple API but is very flexible and very fast. It is very young library but it already has decent popularity (20k stars on GitHub and very steep positive curve on Google Trends) and nice ecosystem of plugins. It kind of solves the same problem as React (both are considered as Views in MV* patterns) but it works different under the hood. If you want to build more complex single page applications you have few Vue plugin libraries. Most notable are vue-router and vuex (FLUX implementation for Vue).
I tried a bit of Backbone, Angular and React before settling with VueJS. For me, it was ease of use that made Vue winner. Now I'm doing personal project with Vue, complex single page application and it's a joy to work with Vue