I would suggest spending your money to get the book. The movie takes a small snapshot in time, from Armstrong’s entry into NASA until Apollo 11, and does fairly well with it.
However, there is much more to his story. A Naval fighter pilot in the Korean War, a test pilot after leaving the Navy and before becoming one of the first two CIVILIAN astronauts. Not to mention his incredible body of work after leaving NASA.
I can understand not doing much with the pre- and post- NASA experience due to time constraints, but they could have done a few minutes at the beginning and an “afterword” crawl like so many fact-based movies do now.
Yes, I did a report on him in High School. I had no idea the man was so accomplished. We all just knew him as the first man on the moon, not that it was small potatoes.