At this point, Flutter is undoubtedly the Major Competitor to React Native. Ryan Edge has documented the detailed comparisons very well in his comment!
To be within the limit of the question asked here, I would say that, Flutter's popularity and adaption has been increased hugely in last 6-8 month. If github stars can be one of the stat factor, in Jan 2019 flutter was at 37K and React Native at 69K. If you compare them today in terms of popularity and growth in it, Flutter is at 71K and React-Native close to 80K.
Flutter is making longer leaps in terms of being popular and becoming major contender to React Native. I am personally a Flutter Fan and enjoy lots of easy integrations with Google Cloud Platform APIs..
Things are going great so far!
Flutter is going to kill React-Native.
- Google is backing it.
- Have you tried the Material Set? There is hardly anything you can not do with it.
- It comes pretty much batteries included. There is no need to import things like React Navigation.
- You can build websites with it as well, and desktop software.
- It is going to be the native language for Google's Fuchsia OS because it is written in Dart.
I don't know if it's the major contender for React Native, but it's definitely a competitor.
Personally, I love it. It's declarative UI syntax is really easy to use, and you don't have to worry a lot about constraints.
However, coming from an HTML/CSS/JS background, React Native was extremely easy to pick up, and I had fun working with it.
I will say that Flutter's system of running the app seems much faster than React Native's, especially with the live update.