In the last five years the European institutional architecture of banking regulation and supervision has undergone sweeping changes, brought about by a number of sequential legislative initiatives. Such a "Copernican revolution" naturally calls for investigating whether and how these different layers of reforms add up to (or can be interpreted in a way that ensure) an overall consistent, efficient and effective design for banking regulation and supervision. This is particularly the case for the European Banking Authority (EBA) and the Banking Union (BU), two new institutional players which in the public debate are sometimes dubbed as overlapping or even conflicting. The paper provides a critical analysis of this interplay and its components, also with the aim to provide food for thought for further exploration, from a private as well as a public law perspective. It starts from the reasons behind the foundation of the EBA and the BU, to show how these new institutional players in fact were created to pursue two distinct and complementary goals, and operate on two separate but interconnected institutional levels. The paper then dwells on the panoply of innovative regulatory tools which the EBA can dispose of in order to accomplish its mission to foster maximum harmonization and the creation of a single set of common rules (the "Single rulebook" or SR): technical standards, guidelines and recommendations, and other "soft law" instruments, such as the Q&A tool. The analysis aims to stimulate further critical thinking on the scope and possible impact of these tools, and their consistency within the overall European framework of legal sources. Hence, the focus moves on the main areas covered by the SR (i.e. prudential rules and resolution) and the priorities followed in its build up, highlighting how these priorities can contribute to the effective functioning of the two current components of the BU, i.e. the SSM and the SRM. The paper concludes with some remarks on areas of possible improvement and development, underlining the need to: i) step up the harmonization of corporate and insolvency laws, given their impact on cross-border banking and cross-border resolution; ii) provide more certainty on the scope and possible effects of EBA's mediation role; iii) rethink the governance of the EBA, if one wants to get to a more balanced interplay between national and European drivers.