Gene is competitive. We see his competitive drive early on in the novel as he strives to outdo Finny in any way he can. This proves difficult in most areas as Finny is a lively, funny, charming and physically gifted person. With no chance at winning a competition in personality and athletics against Finny, Gene turns to academics and finds that he can prevail there.
Gene is also occasionally reckless and impulsive. While he may be both less reckless and less impulsive than Finny, Gene's spontaneous actions have an enormous impact on his life and Finny's as well.
At one point, Gene he bounces a tree branch and causes Phineas to fall, breaking his leg, ending his chances at going to the Olympics and leading ultimately to his death. Gene's impulsive act seems to stem from his competitive nature. There is also a hint of vindictiveness in Gene that is aimed at Finny for no reason beyond the the fact that Finny was confident and basically good, without needing to doubt himself.
"Although he is a capable athlete and an excellent student, Forrester is unable to prevent the dark side of his inner self from perverting and distorting his enjoyment of the world and the people around him" (eNotes).
Why is Gene impulsive and competitive? These traits could arguably come from a more fundamental emotional lack in Gene. He may suffer from a lack of self-esteem that causes him to fixate on how he compares to Finny and to lash out at others (often in passive-aggressive ways).
Gene is also ruminative, reflective and remorseful. He thinks about his identity and his actions with a fixed and focused mindfulness that ultimately brings him to maturity, but not before he realizes what he has done to Finny and how he has failed morally. In one of his final reflections, Gene continues to compare himself to Finny and finds that he is like all the others, incapable to maintaining an inner harmony as Finny did.
"All the others at some point found something in themselves pitted violently against something in the world around them. [...] When they began to feel that there was this overwhelmingly hostile thing in the world with them, then the simplicity and unity of their characters broke and they were not the same again."
Gene's intelligence and reflective nature are both on display in this passage. His tendency to be observant and insightful are seen here too, though the irony of his behavior is illuminated in such a passage as well. He could size up others easily enough, but failed to understand himself enough to consciously choose how to act. He was driven by impulse and emotional need without fully recognizing this or coming to terms with it.