For a sample of nine well-studied giant ellipticals, we compare the projected radial distribution of their red and blue globular cluster (GC) subpopulations with their host galaxy stellar and X-ray surface brightness profiles. We support previous findings that the surface density distribution of red (metal-rich) GCs follows that of the host galaxy starlight. We find good agreement between the outer slope of the blue GC surface density and that of the galaxy X-ray emission. This coincidence of projected radial profiles is likely due to the fact that both blue GCs and X-ray emitting hot gas share the same gravitational potential in equilibrium. When deprojected the X-ray emitting hot gas has a radial density dependence that is the square root of that for the GC density. We further show that the energy per unit mass for blue GCs is roughly half that of the hot gas.