In the Howard/Brando version, Bligh is portrayed as a ridiculous cartoon villain who takes delight in tormenting his crew members, so pretty much any film based on the events on the Bounty is bound to be more fair and accurate than that film.
What the movie gets right is the fact that Bligh was a brooding loner with poor interpersonal skills and a bad temper, but at the same time was basically fair: by all rights he could have hung Churchill and the other deserters, instead he just had them flogged. It also was accurate in portraying Christian as an immature and ultimately selfish man who put his infatuation ahead of his duty.
There is an account of Bligh's later service in Australia where pretty much the same thing happened to him--the people who served under him rebelled and he was found by the authorities hiding under a bed. But...I liked this version--it's the best of the three movies and I was disappointed by the critical response when it came out in 1984. A very well-made film with good use of Vangelis music. Hopkins was excellent as Queeg. I mean Bligh.