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!