Wired and wireless access networks continue to evolve toward higher-capacity, multi-service systems. Recent wireless broadband networks such as 3G LTE and WiMax provide a general-purpose IP platform with over-the-top services at the application layer, which is similar to the design of wired IP platform networks. This paper examines whether wired and wireless access networks are likely to converge on a common architecture, or if not, whether wireless networks are likely to converge on a common wireless architecture. We conclude that the answer to both questions is No. We identify fundamental and persistent differences between wired and wireless networking that will propel wired and wireless access network architectures on divergent evolutionary paths. Whereas we expect wired broadband access networks to continue to evolve toward a common general-purpose platform architecture, we expect wireless networks to remain heterogeneous. The inherent scarcity of radio frequency spectrum emerges as the key reason for this prediction. We examine the implications of divergent evolutionary paths for market structure and regulatory policy.