The coarse spatial resolutions of hyperspectral (HS) satellite images limit their use in many applications. The spatial structure quality of HS images can be improved by fusing them either with higher-resolution panchromatic (PAN) images, or with higher-resolution multispectral (MS) images. Fusion of HS images can be done with fusion methods that are designed to fuse MS and PAN images, and the fusion methods developed for the fusion of HS and MS images. A wide variety of HS-MS and MS-PAN image fusion techniques can be used for the fusion of HS images, which leads the users to a hesitation as to which method(s) should be used for optimal fusion performance. Hence, the current study aimed to qualitatively and quantitatively assess the HS image fusion performances of a total of 15 MS-PAN image fusion methods and 17 state-of-the-art HS-MS image fusion techniques within four experiments, with the hope to give some clues on the performances of the fusion techniques used. Experiments showed that the HS-MS fusion methods exhibited much better HS image fusion performance, compared to the MS-PAN fusion methods used. It was also concluded that the coupled nonnegative matrix factorization (CNMF), convolutional neural network (CNN) denoiser-based method (CNN-D), HS super-resolution (HySure) and fast fusion based on Sylvester equation with naive Gaussian prior (FUSE-G) techniques provided the most robust fusion results.