Chromotomography is a form of hyperspectral imaging that uses a prism to simultaneously record spectral and spatial information, like a slitless spectrometer. The prism is rotated to provide multiple projections of the 3D data cube on the 2D detector array. Tomographic reconstruction methods are then used to estimate the hyperspectral data cube from the projections. This type of system can collect hyperspectral imagery from fast transient events, but suffers from reconstruction artifacts due to the limited-angle problem. Several algorithms have been proposed in the literature to improve reconstruction, including filtered backprojection, projection onto convex sets, subspace constraint, and split- Bregman iteration. Here we present the first direct comparison of multiple methods against a variety of simulatedtargets. Results are compared based on both image quality and spectral accuracy of the reconstruction, where previous literature has emphasized imaging only. In addition, new algorithms and HSI quality metrics are proposed. We find the quality of the results depend strongly on the spatial and spectral content of the scene, and no single algorithm is consistently superior over a broad range of scenes.