If you always feel a need to prove that you are as successful or even better than your partner, you are competing with him or her.
In a healthy relationship, the partners complement each other. They bring their strengths to bear on the relationship to make it succeed. They both realise they have weaknesses in one form or another and as such they use their strengths to compensate for the weakness of one another, thereby building a stronger relationship.
No matter what you experienced in the past that may have contributed to your competitive spirit, put it behind you! Leave the past in the past and focus on the future!
If you are always trying to prove yourself to gain acceptance from your partner, two things are involved, either your mind is playing games with you or you are in an unhealthy relationship.