Jak evolves drastically as a character over the course of the series. During The Precursor Legacy, he is presented as brave and curious, willing to throw himself into dangerous situations. After being subjected to Dark Eco treatments for two years at the hands of Baron Praxis, revenge is his main motive, and he has become angry and reckless - this is only exacerbated by the presence of the Dark Eco in his system. He also takes some enjoyment in killing Metal Heads and a fondness for guns. Nonetheless, Jak does retain some heroic personality traits.
which sees him gain Light Eco powers to balance the Dark Eco, sees him become less angry and more mature; this was almost certainly aided by the death of his father. Later in some racing event, shows him has having relaxed somewhat (due to the balancing effect of Light Eco), though this final encounter with Mizo shows that the anger still exists under the calmer exterior. In TLF, he seems to be more carefree and happy. Despite some scenes hinting his anger (i.e. when he tries to turn to Dark Jak, seeing the Dark Warrior Program chair, etc.) he seems to be more cheerful, particularly around the time he finds out about Dark Daxter, and more like his old self from TPL.
Daxter is a cowardly character who always hides behind Jak's back and always tries to refuse facing some danger. Before Jak goes on to fight with Klaww, Daxter says "I'll stay here and protect Keira! Jak, I think you're ready to take on that monster without me. " or before Jak goes to the Metal Head Tower he says "I'll stay here and... protect Sig!". But in Daxter (the game) his heroic nature was revealed, showing that if he has no one to protect him, he can protect himself and that his friendship with Jak is undying. On rare occasions, Daxter proves heroic even in the presence of Jak. Most notably in Jak III after Count Veger taunted Jak about Damas being his father. He also does it again while going down into the catacombs, as he shouts "Lets get him!".
Daxter, for the most part, is almost never serious and constantly goofs around. But he's always supportive of Jak, especially when he really needs it. Daxter says many memorable lines, perhaps his most famous being, "Stay fuzzy, save the world. Choices." from the end of Jak and Daxter: The Precursor Legacy. Daxter has many nicknames for certain characters, particularly Samos and Krew. He also finds himself at odds with other characters, especially Samos in the first game, but also with Krew and Pecker. Daxter will find himself insulted plainly by Samos (one prime example of that is when Jak and Daxter show up from Misty Island in the intro, Samos says that even if he could turn Daxter back into a human, he wouldn't do so, saying that Daxter's having been turned into an Ottsel is actually an improvement) and won't respond back to him. Samos obviously begins to do this after tiring of putting up with Daxter for so long. Samos insults Daxter to such a high level in that when Jak and Daxter meet The Shadow (the younger Samos) in Jak II (who does not recognize the heroes), he says to Daxter, "I never forget a face, especially one that ugly". The only response on Daxter's part is to quietly say to himself, "So it begins." However, when it counts, Samos reminds both Jak and Daxter how they are true heroes. Interestingly enough, when Daxter says "So it begins.", he doesn't know that it is the young Samos, a minor loophole in the story.
Daxter taking role on tutoring a sentinel cadet at the academy while he still hanging out with Jak whenever there's a mission.