I'd like to find a word to describe someone who, in no matter what situation, wants to be the best. Even if the topic is something negative (such as being told he is insane) he will want to be considered the best at displaying that negative trait (he would want to be the most insane person around).
That person is a one upper. Courtesy of urbandictionary:
An annoying person who responds to hearing someone else’s experience or problem by immediately telling a similar story about themselves with a much more fantastic (or terrible) outcome.
Person: I got to meet James Hetfield before the concert and I got his autograph.
One Upper: Yeah, well my cousin knows the head of security for Metallica, and he got us front row tickets to the show and then we went backstage and met the whole group. Then they invited us back to their hotel room and we partied with them all night.
Person: I have a a dislocated knee.
One Upper: Yeah, well last summer I broke my leg in four places and had to have a steel pin inserted. I also had to have surgery done on my knee to repair the torn ligaments. I was on crutches for almost two months.
How about competitive, hypercompetitive, or driven?
competitive: having or displaying a strong desire to be more successful than others.
hyper-: over; beyond; above.
driven: (of a person) relentlessly compelled by the need to accomplish a goal; very hard-working and ambitious.
Hypercompetitive probably best captures the sense you're seeking: over-the-top competitive.
Perfectionist comes to mind: a person who is only satisfied if what he is doing is perfect. (http://www.thefreedictionary.com/perfectionist)
As a psychological trait, perfectionism can be a compulsion to do everything perfectly, regardless of whether it's positive or negative.
Perfectionists are driven by internal standards. If you mean relative to others, competitive might describe that:
If you're competitive, you want to be the best.