We propose a novel generic information-theoretic framework for characterizing the task difficulty in the Collective Perception paradigm. Our formalism builds on the notion of Empowerment - a task-independent, universal and generic utility function, which characterizes the level of perceivable control an embodied agent has over its environment. Series of simulations with an empowerment model of the collective perception scenario revealed a significant correlation between the levels of empowerment and the accuracy demonstrated by a set of standard collective decision-making strategies and a recent state-of-the-art neural network controller on nine benchmark patterns, used previously for assessing swarm performance. The results elucidate the key role of both the agent embodiment and the environmental pattern in characterising task difficulty, and justify the application of empowerment to analytically assess this role, which could help predict swarm performance and support the development of more efficient decision-making strategies.