Biomaterials have significant functions as tissue scaffolds to support cells for regeneration. Nanofibrous scaffolds which mimic the architecture of the extracellular matrix are well suited to support epithelial cells for ocular tissue engineering. This study aimed at investigating the role of scaffold architecture, if any, on the response of ocular epithelial cells. Thus, we have cultured two different types of ocular epithelial cells on nanofibrous scaffolds of two different diameters to evaluate their generic and cell-specific properties. Human adult retinal pigment epithelial (ARPE-19) and human corneal epithelial (HCE-T) cells were cultured on poly(ε-caprolactone) (PCL) nanofibers of different diameters, nominally 500 and 1300 nm. Moduli of the fiber mats were marginally different at 7.4 and 11.1 kPa for 500 and 1300 nm diameter, respectively. The molecular changes in the cells in response to the different fibers were analyzed by qRT-PCR, Western blot, immunofluorescence, ELISA, flow cytometry, MTT assay, and SEM to assess properties such as proliferation, apoptosis, membrane potential, epithelial-mesenchymal transition, stem cell population, VEGF-A secretion, differentiation, and metabolic status of the cells. HCE-T cells revealed characteristic morphology along with higher expression of proliferation, differentiation, and lower apoptotic markers when cultured on PCL nanofibers of 500 nm. However, on nanofibers of 1300 nm, the cells showed higher expression of the corneal stem/progenitor as well as pluripotent stem cell markers. ARPE-19 cells exhibited characteristic hexagonal morphology with elevated expression levels of proliferative markers, phagocytic activity, and lower apoptosis levels. However, on 500 nm nanofibers, they expressed higher levels of pluripotent markers and secretion of VEGF-A. These findings demonstrate that the response can differ markedly from scaffold architecture even if derived from the same tissue and originating from the same germ layer. Furthermore, it paves the way for a target specific outcome and, thereby, for personalized translational medicine.