Peter is first and foremost, a big brother, and he takes this responsibility very seriously. He makes it his priority to look after his siblings, especially Lucy in LWW, as she was very young at the time. He went into near shock when he thought they lost Lucy at the waterfall. Peter also shows great worry when Edmund goes off on his own to see the White Witch. During the Battle of Beruna, he told Edmund to get himself and their sisters home.
Peter has also been known to be quite stubborn and lose his temper. He gets into a lot of arguements with both Susan and Edmund, although it's more of scolding for the latter. In LWW, he calls Edmund a little beast [the book], and a little liar [the movie] after he found out that Edmund had lied about going to the wardrobe and thus hurt Lucy's feelings. He had a hard time adjusting back in his own world, constantly getting in fights. He was too stuborn to accept that he was just a kid. In PC [the movie], he and Caspian start off on the wrong foot as he couldn't fully accept handing his kingdom over to another ruler. Peter argues with Caspian over battle strategy, and has a hard time accepting that it was as much his fault as Caspian's that the raid on the castle failed [Movie]. He also refused to listen to Lucy about seeing Aslan and then continued to disregard the ruth in her words when they were palnning to raid Miraz's castle. In spite of this issue, he is usually ready to take all of the blame, as in LWW when he admits that he shouldn't have been so hard on Edmund. He also feels guilty for not better protecting his brother.
Peter is an emotional being, sometimes letting his emotions cloud his better judgement. In the beginning of PC [movie], he got in a fight with some boys because they made him do something he didn't want to. When raiding Miraz's castle, he refused to call off the troops because he was angry and wanted revenge on the Telmarines for invading his country.
Despite this, Peter is truly magnificent, and gives one the sense of being around royalty when one is with him. He has good leadership skills, and finds it easy to lead an army into battle. In PC [book], Capsian was in awe of him after they met, and was more than willing to follow his leadership. He is always ready to take responsibility for his actions. After doing some growing up in PC, he readily and humbly accepted that he can longer return to Narnia, this time withous spite and anger.
In LB, he is the one who stops the gossip about Susan before it can go any farther, and he is the one who says it must certainly be allowed to eat the fruit on the trees.
All in all, Peter's good traits seem to outweigh his bad.