Memory decline associated with physiological aging and age-related neurological disorders has a direct impact on quality of life for seniors. With demographic aging, the assessment of cognitive functions is gaining importance, as early diagnosis can lead to more effective cognitive interventions. In comparison to classic paper-and-pencil approaches, virtual reality (VR) could offer an ecologically valid environment for assessment and remediation of cognitive deficits. Despite the rapid development and application of new technologies, the results of studies aimed at the role of VR immersion in assessing cognitive performance and the use of VR in aging populations are often ambiguous. VR can be presented in a less immersive form, with a desktop platform, or with more advanced technologies like head-mounted displays (HMDs). Both these VR platforms are associated with certain advantages and disadvantages. In this study, we investigated age-related differences related to the use of desktop and HMD platforms during memory assessment using an intra-subject design. Groups of seniors (N = 36) and young adults (N = 25) completed a virtual Supermarket Shopping task using desktop and HMD platforms in a counterbalanced order. Our results show that the senior performances were superior when using the non-immersive desktop platform. The ability to recall a shopping list in the young adult group remained stable regardless of the platform used. With the HMD platform, the performance of the subjects of both groups seemed to be more influenced by fatigue. The evaluated user experiences did not differ between the two platforms, and only minimal and rare side effects were reported by seniors. This implies that highly immersive technology has good acceptance among aging adults. These findings might have implications for the further use of HMD in cognitive assessment and remediation.