Different forest types based on different tree species composition may have similar spectral signatures if observed with traditional multispectral satellite sensors. Hyperspectral imagery, with a more continuous representation of their spectral behavior may instead be used for their classification. The new hyperspectral Precursore IperSpettrale della Missione Applicativa (PRISMA) sensor, developed by the Italian Space Agency, is able to capture images in a continuum of 240 spectral bands ranging between 400 and 2500 nm, with a spectral resolution smaller than 12 nm. The new sensor can be employed for a large number of remote sensing applications, including forest types discrimination. In this study, we compared the capabilities of the new PRISMA sensor against the well-known Sentinel-2 Multi-Spectral Instrument (MSI) in recognition of different forest types through a pairwise separability analysis carried out in two study areas in Italy, using two different nomenclature systems and four separability metrics. The PRISMA hyperspectral sensor, compared to Sentinel-2 MSI, allowed for a better discrimination in all forest types, increasing the performance when the complexity of the nomenclature system also increased. PRISMA achieved an average improvement of 40% for the discrimination between two forest categories (coniferous vs. broadleaves) and of 102% in the discrimination between five forest types based on main tree species groups.