Competitive competition is between mutual antagonists. The parties have opposing aims, and they exert their wills in opposition to one another. Competitive competition expends common resources and diminishes the capacity of both parties.
Cooperative competiton is between mutual protagonists. The parties have a common aim, namely to improve their skills or capacity, and they cooperate in providing each other with a mutual challenge. Cooperative competitition expands common resources and increases the capacity of both parties.
When discussing the value of competition, it is important to distinguish between these two types.