The ubiquitous connectivity between vehicles and smart transportation infrastructure will facilitate the information flow necessary for empowering smart service for efficient, safe, and eco-friendly transportation of people and goods. Although vehicular communication technologies is quickly advancing toward ubiquitously connected cars, the design of networking protocols for such vehicles is still in its infancy, facing multiple daunting challenges. In this article, we advocate for the use of the information-centric networking (ICN) paradigm for the full realization of connected cars, that is, the integration of both in-car computing systems and the car-to-digital world. We discuss the emerging challenges for the design of ICN-based protocols for connected cars, and we formally put the current debate into perspective regarding which transmission mode (broadcast or unicast) should prevail for the design of such protocols. Concerning this debate, we propose to classify recent and representative protocols in broadcast and unicast-oriented solutions, and we highlight the trade-offs of each approach. Based on a critical qualitative evaluation, we advocate that adaptive and hybrid approaches would perform better for information- centric connected cars. Hence, we provide a guideline for the further design of ICN-based protocols for connected cars. Finally, we discuss some future research directions that might be considered to advance the process of content distribution in connected cars.