Adaptational Angst Upgrade: Book!Carter is a very straight-up heroic type. Movie!Carter starts out embittered after the Civil War and not wanting much to do with anyone, until he finds his inner hero on Mars.
Chronic Hero Syndrome: If John sees someone is in serious danger he will intervene on there behalf, he just can't help himself.
Desperately Looking for a Purpose in Life: He seems a bit wayward at first, and even when he first shows up on Mars, the only real thing he wants to do is go back home. Then he starts getting attached to the Tharks as well as Dejah...
The Chains of Commanding: He takes his role as Jeddak of the Tharks very seriously, but having to continually live up to the downright brutal expectations of a Green Martian leader plainly wears heavily on him.
Composite Character: In the book, the leader of the Thark horde that Carter falls in with is Lorquas Ptomel; Tars is his second-in-command. As Tars is a much more important character- and Lorquas pretty much drops off the face of Barsoom after a while- Tars gets to take over the leader-role in the film.
Evil Counterpart: To Carter. Both were warriors who found themselves in possession of incredible power, but where Carter at first just wanted to go home, and then used his abilities to save Dejah, Helium, and Barsoom, Sab revels in his power and wants to Take Over the World.
Adaptational Badass: In addition to the Therns as a whole getting a major tech-upgrade, Book!Matai Shang basically sat on his throne and didn't get involved until Carter was already exposing the Therns' false religion. In the movie, he's a much more proactive, Darth Sidious-esque schemer.
Affably Evil: He's not an unpleasant sort to be around, for chessmastering planet-conquering alien godling, and actually seems to enjoy his cat-and-mouse game with Carter. "Your move, earthman."