The efficiency of private sector banks stop the moment an account is opened. Thereafter, both are operating with almost the same efficiency level. The time taken by both public sector banks and private sectors banks to send ATM pin code is almost the same.
Moreover, private sector banks in the name of service have now started charging for almost everything. The only thing that reamins to be charged is "Bank Entry charges".
As you correctly said that it is the process which makes difference however improving of process require investments. Private banks in the name of resource utilisation have not kept pace with upgradation in processes.