An article in the Indonesian paper, Bisnis Indonesia describes how two Islamic banks, Bank Syariah Mandiri and Bank Muamalat Indonesia, dominate the market for Islamic banking, which the paper attributes to "late expansion by other sharia banks on building infrastructure and network as many of them just being spinned off their parent companies recently".
This is an interesting market structure and contrasts to several GCC countries where there are a large number of small Islamic banking companies, which has led to many instances where experts call for greater consolidation. However, in Indonesia, the dominance by two large banks may not necessarily serve the market well when they rely on mudaraba and musharaka more than Islamic banks in other countries.
This is not a criticism of a higher percentage of profit-sharing contracts in Islamic banks. It may benefit the market to have a better balance between the profit-sharing and the debt-based products, if for no other reason than it will provide a clear "difference" between Islamic and conventional banks. However, an IMF study from 2008 found (pdf) evidence that smaller Islamic banks are more stable than large Islamic banks and conventional commercial banks, while large commercial banks were found to be more stable than their Islamic counterparts.
One study does not prove the case; there is a much greater diversity among large conventional commercial banks than there is among large Islamic banks. For example, in contrast to what I expected when I looked back to the study, the Islamic banks (only wholly Islamic banks were considered, not Islamic windows) were larger on average than the conventional banks when measured by total assets. This is contrary to a piece of conventional wisdom that Islamic banks need to grow in size to compete with their conventional competitors, but could also indicate that the sample used in the study does not include the "mega" banks, the conventional international financial behemoths that many people see as competition for Islamic banks.
However, returning to the impact of size on stability, the authors of the IMF report, Cihak and Hesse, posit that the larger an Islamic bank gets, the harder it is to manage risk. This is likely to be particularly true as the size of the bank's profit-sharing portfolio increases, which leads to my suggestion that a market structure dominated by two large Islamic banks may reduce the overall stability of the Islamic banking system compared to a more balanced one where five or six banks share the bulk of total assets.