To become better (than others)...

...become a better you.

I find that too many of us are competing against the wrong standard.  In fact more than once, I've caught myself comparing myself to others and unintentionally 'competing' against them. The truth is:
To become better, become a better YOU.

The best type of competitiveness is competition against one's self - not anyone else.
The best you can ever be is a better you.
The most successful people in life focus on self-improvement and self-development.
No matter how hard you try, aiming to be a better version of someone else ultimately makes you second-best of the person you're trying to be like - a copy not an original.

Take Judy Garland's advice:

Always be a first-rate version of yourself,

instead of a second-rate version of somebody else.

 

I strongly recommend that you make this one of your resolutions in 2014 and for life.