...or a better person?
Thinking about it, I decided it's much better to be "a better person" - yes, a better version of myself than to "compete" and try to become better than the other person. If you keep trying to be better than others, you'll never succeed...
I've heard people advise - "Be the better person" - especially when there is a rift between 2 people and neither one wants to give in/apologize.
What is good about wanting to be better than say a bully? Are you aiming to be a better bully i.e. better at bullying? You see, wanting to be the better person can make you become better in a bad way. In fact, wanting to be the better person, stems from pride while wanting to be a better person (including apologizing) is an act of humility...which always pleases God.
It's certainly not wrong to want to be a better person. God gave us that desire. ~ @JoyceMeyer