This study presents a comparative analysis of a binary-coded Red Deer Algorithm (RDA) and a binary-coded Genetic Algorithm (GA) across a diverse suite of benchmark problems. The RDA, a nature-inspired metaheuristic based on the mating behaviour of red deer, has shown promise in continuous optimisation but remains underexplored in binary search spaces. We implement and evaluate a binary-coded RDA (bRDA) on both synthetic and real-world combinatorial benchmarks. Performance is assessed not only in terms of final solution quality and convergence dynamics, but also through population diversity analysis over time, offering insights into how each algorithm balances exploration and exploitation throughout the search. Unlike prior studies that report performance using generation count or runtime, we present all results as a function of the number of fitness evaluations, allowing for a fair, implementation-independent comparison. Our findings show that while the GA excels in assembling coherent building blocks, the bRDA maintains greater population diversity early in the search and adapts more effectively to deceptive and heterogeneous landscapes. These results underscore the importance of diversity-aware design and suggest that hybrid algorithms may benefit from combining the GA’s efficient building-block assembly with the RDA’s local refinement.