On the one hand, winning a competition only means that you happen to be the best in a very specific pool of people--it does not actually mean you're the best in the world. There will always be someone better than you.
Is that okay?
In my mind, yes. How else does humankind advance? We are always trying to better ourselves. We can learn from each other, inspire each other, encourage each other to do more. In this collaborative spirit, I feel that we would all benefit from a bit of friendly "one-upping" each other.
If done in the right spirit, competitions can be extremely beneficial to everyone. Competitions have the capacity to be the ultimate form of collaboration, where we all band together to see how great we can all really be.