The rise of Uber as the global alternative taxi operator has attracted a lot of interest recently. Aside from the media headlines which discuss the new phenomenon, e.g. on how it has disrupted the traditional transportation industry, policy makers, economists, citizens and scientists have engaged in a discussion that is centred around the means to integrate the new generation of the sharing economy services in urban ecosystems. In this work, we aim to shed new light on the discussion, by taking advantage of a publicly available longitudinal dataset that describes the mobility of yellow taxis in New York City. In addition to movement, this data contains information on the fares paid by the taxi customers for each trip. As a result we are given the opportunity to provide a first head to head comparison between the iconic yellow taxi and its modern competitor, Uber, in one of the world's largest metropolitan centres. We identify situations when Uber X, the cheapest version of the Uber taxi service, tends to be more expensive than yellow taxis for the same journey. We also demonstrate how Uber's economic model effectively takes advantage of well known patterns in human movement. Finally, we take our analysis a step further by proposing a new mobile application that compares taxi prices in the city to facilitate traveller's taxi choices, hoping to ultimately to lead to a reduction of commuter costs. Our study provides a case on how big datasets that become public can improve urban services for consumers by offering the opportunity for transparency in economic sectors that lack up to date regulations.