A profitable relationship between today’s tech-savvy customers and banks is the primary component for most of the strategies of the banking organizations. So, the main purpose of this research-work is to test the structural paradigm of CRM (Customer Relationship Management) with the effectiveness of e-banking and branch-banking. With a sample size of 518 bank customers through a stratified sampling method, SEM (Structural Equation Modeling) is applied to test the above-mentioned structural relationship after testing two measurement models through CFA. So, this study proceeds with an experimental research design. Major outcomes of the study indicate that the CRM practices of banks have a significant direct effect on the effectiveness of e-banking; along with significant indirect effect through the mediation of the effectiveness of branch banking. Further, customer biases are seen to significantly moderate the above effects, and the model invariance is also successfully tested. Novelty refers to structural relationships among components of both traditional business practices (branch banking) and modern business practices (e-banking) have never been studied prior to this research work having CRM as its context. Practical implications say that the structural relationship along with testing results of moderation effect of customers’ biases and model invariance is providing innovative input for marketing strategies of banking products/services. Further, results of this study can create social awareness regarding concerns of banks regarding economic development of society. Rather than taking bank-customers’ opinion only, the bank-employees’ inputs alongside would be strengthening the research outputs.