I think the biggest pros of react native are:
1) Not having to compile to see UI/Business logic changes (Swift compiler is slow).
2) The ability to push changes over the air after you switch.
3) Large parts of your app just work cross platform with minimal changes (I've shipped two iOS/Android apps).
4) If you have a react web team, they can now review and help out with your mobile apps.
5) It's easy to keep product in synch across multiple platforms (i.e android/iOS release at the same time).
I think the big cons are:
1) It's Javascript.. ES6 + babel makes this a lot less terrible than it was in the days of web apps wrapped as native apps but it's still Javascript.
2) If you have to do long running background tasks (network polling, bluetooth, music, location, etc) you basically have to do it in native code. This can be a big architectural pain in the ass depending on what your app does.
3) Ramp up time. Learning about React and all the third party libraries (Redux, etc) you will need to be productive takes time.
4) Cross platform testing. I.e if you share code with your web/android engineers, they will need to be disciplined about not breaking things (npm and versioned shared libraries helps with this).
5) Third party library quality in Javascript land can vary a lot. This requires you spend quite a bit of time vetting them.
If your based in the Bay Area I'm going to be giving a talk on on some of this in March.