The debate on whether Islamic banks (IBs), given their unique attributes and business model, outperform their conventional counterparts in the context of a dual banking system has been ignited, with no conclusive evidence yet reached. This study conducts a comparative empirical analysis of performance between IBs and conventional banks (CBs) in the dual banking system of Malaysia. It investigates whether banks’ performance in Malaysia has been driven by market structure or efficiency. It also investigates whether bank managers have been demotivated and settled for a quiet life due to market power or have been aggressive due to the search for efficiency and market share. Further, it investigates how concentration within one sector influences its counterpart’s performance. Generalised Method of Moments (GMM) and Data Envelopment Analysis (DEA) techniques are employed. The findings revealed that Efficient Structure (FS) and Structure-Conduct-Performance (SCP) hypotheses are rejected for all categories. The Quiet Life Hypothesis (QLH) is accepted for CBs, implying persistency of profits and validity of the Relative Market Power (RMP) hypothesis; however, it is rejected for IBs, implying IBs’ pursuit of market power. Islamic banking sector structure showed no influence on the performance of both IBs and CBs, while CBs negatively influenced the performance of both types of banks and the sector at large. Policy markets can capitalise on the findings, regulators, and banks’ managers to promote performance, efficiency, and set merger policies.