With the emergence of ever-growing smart vehicular applications and ubiquitous deployment of IoT devices across different architectural layers of Intelligent Transportation System (ITS), data-intensive analysis emerges to be a major challenge. Without powerful communication and computational support, various vehicular applications and services will still stay in the concept phase and cannot be put into practice in the daily life. In this paper, we consider the case of Electric Vehicle (EV) to Smart Grid (SG) integration. The EVs are key players for Transport Oriented Smart Cities (TOSC) as they help cities to become greener by reducing emissions and carbon footprint. We analyze different use-cases in EV to SG integration to show how Big Data Analytics (BDA) platforms can play a vital role towards successful EV rollout. We then present two computing platforms namely, distributed cloud computing and edge/fog computing. We highlighted the distinguishing features of each towards supporting BDA activities in EV integration. Finally, we provide a detailed overview of opportunities, trends, and challenges of both these computing techniques.