Assuming that commercially operating public and private sector banks offer analogous banking products and apply analogous banking procedures, including credit procedures, creditworthiness testing methodologies, credit risk management instruments, etc., it is worth using the profitability ratios of specific banking products in the comparative analysis banking performance indicators, financial liquidity ratios, asset and liability management ratios, debt ratios of certain categories of banking assets, specific reserve ratios, security ratios related to credit and operational risk management, indicators related to the efficiency of managing online banking systems and cybercrime risk.
You can create efficiency metrics by utilising input (e.g.: operating expense, staff)..and output (revenue, clients, profit...) to make comparable analysis between banks.