Light field rendering promises to overcome the limitations of stereoscopic representation by allowing for a more seamless transition between multiple point of views, thus giving a more faithful representation of 3D scenes. However, it is indisputable that there is a need for light field displays on which the data can be natively visualised, fuelled by the recent innovations in the realm of acquisition and compression of light field contents. Assessing the visual quality of light field contents on native light field display is of extreme importance in future development of both new rendering methods, as well as new compression solutions. However, the limited availability of light field displays restrict the possibility of using them to carry out subjective tests. Moreover, hardware limitations in prototype models may lessen considerably the perceptual quality of experience in consuming light field contents. In this paper, we compare three different compression approaches for multi-layer displays, through both objective quality metrics and subjective quality assessment. Furthermore, we analyze the results obtained through subjective tests conducted using a prototype multi-layer display, and a recently-proposed framework to conduct quality assessment of light field contents rendered through a tensor display simulator in 2D screens. Using statistical tools, we assess the correlation among the two settings and we draw useful conclusions for future design of compression solutions and subjective tests for light field contents with muti-layer rendering.