In recent years, two pricing policies are commonly adopted by on-demand delivery service platforms (e.g., Meituan PaoTui and Costco) that provide delivery services to heterogeneous customers via self-scheduling providers. One called "transaction-based" pricing policy (TBPP) allows the platforms to determine a per-service wage paid to providers and a price charged to customers for each transaction. The other one called "membership-based" pricing policy (MBPP) also allows the platforms to announce a wage paid to providers but charge customers a membership fee for using an unlimited number of the services in a certain period (e.g., one month). This paper considers an on-demand delivery service platform with self-scheduling providers and two classes of customers (i.e., regular and frequent customers). We aim to analyze and compare the platform's profits and welfare performances generated by the two pricing policies. If the number of regular customers and their preference for TBPP equal the number of frequent customers and their preference for MBPP, respectively, we show that compared with the MBPP, employing the TBPP is beneficial for the platform but is detrimental for customers and providers. However, adopting the MBPP (TBPP) can simultaneously benefit the platform, customers and providers if frequent customers' preference for MBPP is higher (lower) than regular customers' preference for TBPP or the number of frequent customers is larger (less) than regular customers.