Oh that's tough one. But I think I am sold one The Patriot

If you are talking Mel Gibson movies, then I choose the original Mad Max over either of them. Even the first Deadly Weapon was better than either of those two.

If it a comparison of Mel Gibson's acting in the 2 movies, then I believe that he did a better job and there was a better script for Braveheart than The Patriot -- especially since there was also more humor in it.

However, if you are looking for the one that is more historically accurate, then it is The Patriot. -- though this is only because the character in this one is a fictional character rather than focusing on the life of a real person and the writing was majorly inaccurate historically about the individual and many of the other historical elements in the movie. There were a lot of historical errors in the movie The Patriot, but since the lead character is a fictional character, then it is not as bad that a lot of the historical material from the Revolutionary War is not historically accurate. So, it is a "winner" historically because with the fictional leading character it was not as historically flawed as when the focus is a lead character who was a real person.