Adaptive networks consist of a collection of nodes that interact with each other on a local level and diffuse information across the network to solve estimation and inference tasks in a distributed manner. In this work, we compare the performance of two distributed estimation strategies: diffusion and consensus. Diffusion strategies allow information to diffuse more thoroughly through the network. The analysis in the paper confirms that this property has a favorable effect on the evolution of the network: diffusion networks reach lower mean-square deviation than consensus networks, and their mean-square stability is insensitive to the choice of the combination weights. In contrast, consensus networks can become unstable even if all the individual nodes are mean-square stable; this does not occur for diffusion networks: stability of the individual nodes ensures stability of the diffusion network irrespective of the topology.