We compare and contrast the stellar structures of isolated Local Group dwarf galaxies, as traced by their oldest stellar populations, with the satellite dwarf galaxies of the Milky Way and M 31. All Local Group dwarfs with Mv †â6 and ÎŒo < 26.5 mags arcsecâ2 are considered, taking advantage of measurements from surveys that use similar observations and analysis techniques. For the isolated dwarfs, we use the results from Solitary Local (Solo) Dwarf Galaxy Survey. We begin by confirming that the structural and dynamical properties of the two satellite populations are not obviously statistically different from each other, but we note that there many more satellites around M 31 than around the Milky Way down to equivalent magnitude and surface brightness limits. We find that dwarfs in close proximity to a massive galaxy generally show more scatter in their Kormendy relations than those in isolation. Specifically, isolated Local Group dwarf galaxies show a tighter trend of half-light radius versus magnitude than the satellite populations, and similar effects are also seen for related parameters. There appears to be a transition in the structural and dynamical properties of the dwarf galaxy population around âŒ400 kpc from the Milky Way and M 31, such that the smallest, faintest, most circular dwarf galaxies are found closer than this separation. We discuss the impact of selection effects on our analysis, and we argue that our results point to the significance of tidal interactions on the population of systems within approximately 400 kpc from the MW and M 31.