The difference is that React is much less opinionated. You can tie it into your existing Backbone app or you can use Flux (or one of the many Flux-like libraries out there) or you can use Redux (which is in many ways exactly like React, but for state) or you can use something like Relay or Falcor or even something entirely different.
Angular wants to own your project. That's not necessarily a bad thing because it also means you don't need to evaluate the relative pros and cons of lots of tools doing what it already gives you for free and you're more likely to find help because there are more people with your specific combination. But it also limits how much you can adapt Angular to your specific application's needs.
The more you deviate from the defaults, the more you lose the benefits of using a full-featured framework in the first place and the more you have to muck around trying to bend all the parts into the shape you want.
Plus you actually CAN use React inside Angular (or vice versa) if you really want to. It's probably not a good idea because React doesn't do anything Angular can already do (but differently), but it's entirely possible (just like how people already used Angular with Polymer or Backbone or what have you).
I wouldn't say React influences the rest of your app as much as Angular (or Ember) necessarily does but saying that a tool will influence the rest of the app is almost tautological -- every decision affects other decisions, even if it's only because of the mental models it may bring with it.
The truth is, it's not a decision between Angular or just React. You're not going to simply use React. You're going to use React plus something else. That's simply a set of decisions choosing a framework won't require you to make.
The comparison isn't meaningless because there is no either-or choice. The comparison is meaningless because it's incredibly hard to compare just React with all of Angular (or Ember or whatever).
Angular wants to own your project. That's not necessarily a bad thing because it also means you don't need to evaluate the relative pros and cons of lots of tools doing what it already gives you for free and you're more likely to find help because there are more people with your specific combination. But it also limits how much you can adapt Angular to your specific application's needs.
The more you deviate from the defaults, the more you lose the benefits of using a full-featured framework in the first place and the more you have to muck around trying to bend all the parts into the shape you want.
Plus you actually CAN use React inside Angular (or vice versa) if you really want to. It's probably not a good idea because React doesn't do anything Angular can already do (but differently), but it's entirely possible (just like how people already used Angular with Polymer or Backbone or what have you).
I wouldn't say React influences the rest of your app as much as Angular (or Ember) necessarily does but saying that a tool will influence the rest of the app is almost tautological -- every decision affects other decisions, even if it's only because of the mental models it may bring with it.
The truth is, it's not a decision between Angular or just React. You're not going to simply use React. You're going to use React plus something else. That's simply a set of decisions choosing a framework won't require you to make.
The comparison isn't meaningless because there is no either-or choice. The comparison is meaningless because it's incredibly hard to compare just React with all of Angular (or Ember or whatever).