Large scale surveys of the prominent members of the Local Group have provided compelling evidence for the hierarchical formation of massive galaxies, revealing a wealth of substructure that is thought to be the debris from ancient and on-going accretion events. In this paper, we compare two extant surveys of the M31-M33 subgroup of galaxies; the Pan-Andromeda Archaeological Survey (PAndAS) of the stellar structure, and a combination of observations of the HI gaseous content, detected at 21cm. Our key finding is a marked lack of spatial correlation between these two components on all scales, with only a few potential overlaps between stars and gas.The paucity of spatial correlation significantly restricts the analysis of kinematic correlations, although there does appear to the HI kinematically associated with the Giant Stellar Stream where it passes the disk of M31. These results demonstrate that that different processes must significantly influence the dynamical evolution of the stellar and HI components of substructures, such as ram pressure driving gas away from a purely gravitational path. Detailed modelling of the offset between the stellar and gaseous substructure will provide a determination of the properties of the gaseous halo of M31 and M33. ; Comment: 11 pages, 6 figures. Accepted for publication in the Astrophysical Journal. Figure quality reduced. High quality version available at http://www.physics.usyd.edu.au/~gfl/Arxiv_Papers/PAndAS_Mist/