This paper examines how efficiency dynamics of Islamic and conventional banks compare and how they are converging across different countries. We employ both parametric and non-parametric methods to analyse a panel of Islamic and conventional banks from 23 countries during the period 1999 to 2014. Parametric methods (stochastic frontiers methods) shows that both steady state efficiency and the speed of convergence of Islamic and conventional banks are similar. A non-parametric framework (classification trees) identifies a varying degree of alignment between the Islamic and conventional banking model across countries, which could explain the plurality in conclusions in the Islamic/conventional bank efficiency debate. We find that the alignment between the two bank types is positively related to the country's financial depth, transparency, economic stability and banking concentration. At the bank level, the alignment in the two banking systems is associated with higher income diversification, liquidity, profitability and financial stability.