You should most definitely look at the docs for both before you decide. Unless something has changed, the Xamarin docs are pretty weak. They seem good until you do something beyond a simple todo list, then you are on your own, with few books/resources to draw from. React on the other hand has a much more active community and thorough docs.

I'm not saying Xamarin won't work for you, plenty of people seem to be productive in it. I personally have switched my focus to React and React-Native (coming from a c#/.net background).

Now I just wish MS would support React as a first class citizen in Visual Studio 2015/Community. It's great it's supported in Code, but lets get it supported across the entire VS family. That would rule.