Cells are integral to all forms of life due to their compartmentalization by the plasma membrane. However, living organisms are immensely complex. Thus there is a need for simplified and controllable models of life for a deeper understanding of fundamental biological processes and man-made applications. This is where the bottom-up approach of synthetic biology comes from: a stepwise assembly of biomimetic functionalities ultimately into a protocell. A fundamental feature of such an endeavor is the generation and control of model membranes such as liposomes and polymersomes. We compare and contrast liposomes and polymersomes for a better a priori choice and design of vesicles and try to understand the advantages and shortcomings associated with using one or the other in many different aspects (properties, synthesis, self-assembly, applications) and which aspects have been studied and developed with each type and update the current development in the field.