Visual discrimination of clinical tissue types remains challenging, with traditional RGB imaging providing limited contrast for such tasks. Hyperspectral imaging (HSI) is a promising technology providing rich spectral information that can extend far beyond three-channel RGB imaging. Moreover, recently developed snapshot HSI cameras enable real-time imaging with significant potential for clinical applications. Despite this, the investigation into the relative performance of HSI over RGB imaging for semantic segmentation purposes has been limited, particularly in the context of medical imaging. Here we compare the performance of state-of-the-art deep learning image segmentation methods when trained on hyperspectral images, RGB images, hyperspectral pixels (minus spatial context), and RGB pixels (disregarding spatial context). To achieve this, we employ the recently released Oral and Dental Spectral Image Database (ODSI-DB), which consists of 215 manually segmented dental reflectance spectral images with 35 different classes across 30 human subjects. The recent development of snapshot HSI cameras has made real-time clinical HSI a distinct possibility, though successful application requires a comprehensive understanding of the additional information HSI offers. Our work highlights the relative importance of spectral resolution, spectral range, and spatial information to both guide the development of HSI cameras and inform future clinical HSI applications.