This study considers a public service system consisting of two service providers with different service capacities and qualities, such as healthcare or transportation systems. Such a system is called a two‐tier service system (TTS). The service provider with higher service capacity and quality charges a higher price and is called a “charge service provider,” denoted by CSP, while the other service provider charges a lower price and is called a “free service provider,” denoted by FSP. We study the TTS where customers prefer the CSP to the FSP in spite of the higher price of CSP. The strong preference of CSP to FSP, which can be due to bounded rationality, leads to imbalanced workload for the TTS which implies an inefficient use of limited resources. Although both can offer a common set of services, the CSP is overly demanded and highly congested, while the FSP is under‐utilized. We first study analytically an extreme case where the preference for CSP is so strong that customers choosing the CSP are delay insensitive and those choosing the FSP are delay sensitive. Then, we extend our analysis to more general cases where customers are delay sensitive in both channels and have asymmetric preferences for service providers. Using a stylized queueing model and equilibrium customer choice analysis, we show that under certain conditions, the two‐tier system may reduce congestion and the total social cost in the system. This study offers social planners the guidance in designing less congested, more cost‐efficient, and sustainable public service systems.