When you are only cooperating with others to get something done, such as a project, you can generally find a certain skill set that you can always contribute to the group, and often as a result fail to improve in other skill sets. If you are competing with other people, even if you are also working with them, you need to be able to work many different skills, and are not only pushed to meet your standards, you are pushed to excel however far you need to out-compete your partner. This is true excellence.
I believe that competition does go farther than cooperation in regards to achieving excellence. While I think that cooperation does work wonders in terms of trying to achieve a goal, sometimes competition does more in terms of creating excellence. I think competition is a good thing that can help people strive for more.
Competition goes farther to achieve excellence than cooperation most of the time. Natural selection is one prime example, competition culls the weak and favors the strong so that the next generation will be stronger. Competition is better for consumers as far as products and services. Monopolies have been shown to be bad for the consumer. Competition will always keep innovation running because only the strong/most innovative survive the competitive market. Cooperation has its place in certain instances, but most of the time competition is the best way.
When you're cooperating with someone, you may feel a lack of motivation and only put in the same effort your partner does. If you both are competing against each other, then each of you will try to outdo one another. This will create a better product and make both people better for it.
When you look at the world as it is right now, competition does drive us to greater amounts of excellence. Excellence as defined by today's society, which I do not agree with. I wish we lived in a world where cooperation was the driving force for excellence. We'd all have a better life.