To be honest, once Facebook strips the messenger app from the main app I'm done using Facebook. I don't want to agree to the new terms and conditions.
I tried it out briefly, and IIRC had some trouble with chat notifications still coming from the main Facebook app. I could turn off notifications for it, but that'd kill all of the other notifications too. Making chat only in Messenger would solve this, if they haven't fixed it already.
I still get the notifications in my original FB app, but when I press "messages," I'm taken to the Messenger app.