"Braveheart" is a funny issue. For some people, they dislike the film because of Mel Gibson, and his many intemperate remarks. Thus, his films are viewed by many in the same way that many now view Woody Allen after the revelation of his relationship with his step-daughter. Others simply don't like the film. I'm personally OK with the film, but I respect either view. That, however, is not what is so odd, in retrospect.
Braveheart won over the following field:
Apollo 13
Babe
Il Postino: The Postman
Sense and Sensibility
Here are films that failed to be nominated for Best Picture that year:
Leaving Las Vegas
Dead Man Walking
Mighty Aphrodite
Toy Story
Braveheart's strongest competitor at the time was probably Apollo 13, although I recall there was a sizable outcry for Babe to get the award. One could make the argument that Braveheart won because it did not actually face the strongest films of that Oscar year. Truth be told, I'd assert that Toy Story should have won -- both for it's highly original story, and for the way it revolutionized animated film.
For me, Gibson's implosion has been sad. I remember him in the golden age of Australian cinema in the late 70s /early 80s in films like Mad Max and Gallipoli. I still love watching The Road Warrior, but my favorite Gibson film is Peter Weir's "The Year of Living Dangerously." (with Sigourney Weaver and an incredible performance by Linda Hunt).