The Bourne movies are interesting because Jason Bourne doesn't fight for his country or any particular cause but instead solely for his own survival. He is forced into an impossible situation; he is hunted down by the CIA all the while having amnesia and not knowing anything about himself except his extensive military training which he is forced to use to survive. Jason Bourne goes to impressive lengths to avoid conflict whenever he can, but when he does finally have to fight the action is exhilarating. There is no slow motion and usually no music during the fight scenes, all we hear is the exaggerated sound effects and grunts. The violent scenes in the movies are swift and in the latter two filmed with a shaky camera and disorienting editing which puts us straight into the thick of battle. Watching Bourne singlehandedly disarm and take down armies of agents and using his smarts and his incredible martial arts skills is amazing to watch.
My favorite fight scene is his with Desh in The Bourne Ultimatum. Unlike some other action movies, which take a more stylized approach to violence, we truly get the sense that these men are actually fighting for their lives and will do anything, including using whatever household objects they can find around them, to survive.
The Bourne series is also very different from many other action movies in that Jason Bourne is constantly weighed down by guilt for killing other people. In The Bourne Supremacy and Ultimatum, we see that he goes to great lengths just to get the chance to apologize to the daughter of one of the people he was assigned to kill. Throughout both movies, we see him constantly expressing grief and psychological torment for the things that he did in his past life as a hired assassin and also for the lives he has to take now to survive.