We use deep wide-field photometry from the Large Binocular Camera to study the stellar and structural properties of the recently discovered Andromeda X and Andromeda XVII (And X and And XVII) dwarf galaxies. Using the mean apparent magnitude of the horizontal branch (HB), we derive distances of 621 +/- 20 kpc to And X and 734 +/- 23 kpc to And XVII, closer by >60 kpc than the previous estimates which were based on red giant branch (RGB) observations. Thus, our results warrant against the use of the RGB tip method for determining distances to systems with sparsely populated RGBs and show how crucial HB observations are in obtaining accurate distances in systems such as these. We find that And X is a relatively faint (M-V = -7.36), highly elongated (epsilon = 0.48) system at a distance of 174 +/- 62 kpc from Andromeda. And XVII is brighter (M-V = -8.61) with an M31-centric distance of 73 kpc which makes it one of the closest satellites to Andromeda. Both galaxies are metal-poor: we derive <[Fe/H]> = -2.2 for And X, while And XVII shows <[Fe/H]> = -2.0, consistent with the relation of higher luminosity dwarfs being more metal-rich. Additionally, both galaxies show considerable intrinsic spreads in metallicity (0.2 and 0.3 dex for And X and And XVII, respectively), consistent with multiple stellar populations.