They wrote the script very much together. That’s just a fact. JJ had final say obviously as he was the director but it was a complete collaboration.
And honestly, JJ’s track record in recent years is far superior to Kasdan’s.
JJ’s track record is that he can’t write endings. He’s great with characters but he sucks at overall story telling. He did great characterizations for the Star Trek films but the stories lack anything of genuine Star Trek and the endings make about as much sense. I literally hate those films. The PT are gold in comparison. I rate TFA as the worst Star Wars movie because of all the flubs that I attribute to JJ and his bad editing decisions as director and his bad input as writer. Rian Johnson at least has a track record of writing good stories that keep audiences interested. JJ’s great at characters and action, but he isn’t a very good story teller. At least Lucas was good at that. Kasdan has a good track record. I have no question on his ability to tell a story which I why I look forward to the Han Solo movie. I’ve liked all of the movies he has written that I have seen.
And there are potential spoilers for TLJ out there. There are some leaked set photos and some juicy plot points that are born out by casting.