A paper by Hadeel Abu Loghod examines the performance difference of Islamic versus conventional banks using the logit statistical tool. This takes a number of factors to predict whether a given bank is conventional or Islamic (based on different characteristics of each). If a factor differs significantly between conventional and Islamic banks, the coefficient on that variable would be statistically different. If there is not a difference, then the coefficient would be insignificant.
The database used in the study is rather old, 2000-2005, but it is probably easier to find statistically significant relationships in data that does not include the financial crisis and after effects. The basic finding of the paper (the one asked in the title) is that Islamic banks do not have a statistically different (better or worse) performance than conventional banks.
This is not surprising because there is great heterogeneity in Islamic banks and between conventional banks. It is also not a surprise because although the products used by Islamic banks are structured differently, they create more or less the same economic outcome. Customers receive financing that they must repay over a set period. Conventional banks charge an interest rate, while the cost of funding in Islamic banking is based on 'profit' from a sale (murabaha) transaction or 'rent' in a leasing (ijara) transaction.
Even in the bank-depositor relationship based on mudaraba, the economic outcome is similar. Depositors put their money into their accounts with the bank. Theoretically they are liable to lose that money if the bank's financing activity is not profitable. However, the shareholders of the bank have the incentive to set up reserve accounts to prevent depositor's losses (because the loss by depositors could spark a run on the bank which would end up wiping the shareholders out. The average ratio of deposits to equity in Islamic banks in the sample was 5:1. The depositors are far more liquid than shareholders; they can demand their funds back and if they did so en masse, it would drive the bank into insolvency in most cases because deposits equal around 70% of total assets. Most of those assets are not liquid and could only be turned into cash at a severe haircut to book value.
In terms of the differences between Islamic and conventional banks, the study found that Islamic banks were more liquid, less leveraged and carried a larger percentage of fixed to total assets. This result makes sense when one considers the overall banking environment in which Islamic banks operate. For the period of the data, there were few if any ways besides inter-bank commodity murabaha or wakala for a bank to find liquidity to meet large depositor withdrawals, where conventional banks can go to either the inter-bank market or the central bank (as lender of last resort). There are also more short-term, liquid assets available to Islamic banks for them to place their excess liquidity with very little risk.
The finding that Islamic banks were less leveraged than conventional banks initially seems to make sense given the conventional wisdom that Islamic banks are more stable than conventional banks and can't leverage themselves using derivatives or other exotic products. However, there really is not a limit inherent in the Islamic banking model that would keep them from leveraging their balance sheet significantly. The explanation could be that Islamic banks take more conservative approaches to leverage either because debt is harder to access (sukuk markets are less developed) or investors are concerned that returns would be lower from a bank's sukuk by virtue of its higher proportion of liquid assets or because of a higher risk of the bank defaulting because of liquidity challenges.
The final finding was that Islamic banks held a higher level of fixed assets as a percentage of total assets than conventional banks. The author ascribed this to the use of murabaha and ijara by Islamic banks. However, most Islamic banks do not carry inventory of goods (for murabaha). The murabaha is designed so that the bank minimizes the risk of holding a physical asset by making the period between when it buys the asset and when it resells it very small, often a few minutes. I am not entirely sure of this point (it is more of an accounting issue), but I suspect that for an ijara, the bank would not account for the asset on its balance sheet even if it were being treated as the lessor (responsible for the maintenance and insurance of the asset) from a Shari'ah perspective. Or the asset would be held off balance sheet.
I thought this was an interesting paper; it limited its focus to one specific area of how conventional and Islamic banks differ. However, it does lead to questions for future research. For example, if Islamic banks hold excess liquidity and are less leveraged than conventional banks, why is their profitability not dented. Put another way, if Islamic banks had access to equivalent liquidity management tools and more access to debt financing, would they increase their returns on equity? Another point for future study would be whether these relationships still hold among Islamic and conventional investment banks, or Islamic and conventional banks during and after the financial crisis with rapid deleveraging occurring particularly in the conventional financial system.
 Abu Loghod, Hadeel. "Do Islamic Banks Perform Better than Conventional Banks? Evidence from Gulf Cooperation Council Countries," Arab Planning Institute Working Paper 1011.