In the application of cooperative coevolution for neuro-evolution, problem decomposition methods rely on architectural properties of the neural network to divide it into subcomponents. During every stage of the evolutionary process, different problem decomposition methods yield unique characteristics that may be useful in an environment that enables solution sharing. In this paper, we implement a two-island competition environment in cooperative coevolution based neuro-evolution for feedforward neural networks for pattern classification problems. In particular the combinations of three problem decomposition methods that are based on the architectural properties that refers to neural level, network level and layer level decomposition. The experimental results show that the performance of the competition method is better than that of the standalone problem decomposition cooperative neuro-evolution methods.