This one is about what they apparently called a miracle - pilot managed to water-land a plane after both engines hot shut down, without losing any of the passengers. The movie depicts those events, and the following investigation.
I like Tom Hanks, so I was interested to see this, and it is a very solid drama. With increased credibility due to the fact that it really happened. And my usual source actually claims that major part of what was shown did indeed happen. Sully's background, crash itself, small family details, even flashbacks. Obviously, movie added dramatization to some things. And since movie needed antagonist, the investigators were made into such thing - that's why none of them is based on real people. To not imply that anyone is a really bad guy in this case. Also, in the movie things happen fast, while the real investigation lasted for a very long time.
But yes, most of what is shown is as true as things can be in a movie, and no wonder - this is a recent event, and the movie director had possibility to talk to most participants of this.