  The two most recently published potential energy surfaces (PESs) for the
HeH$_2$ complex, the so-called MR (Muchnick and Russek) and BMP (Boothroyd,
Martin, and Peterson) surfaces, are quantitatively evaluated and compared
through the investigation of atom-diatom collision processes. The BMP surface
is expected to be an improvement, approaching chemical accuracy, over all
conformations of the PES compared to that of the MR surface. We found
significant differences in inelastic rovibrational cross sections computed on
the two surfaces for processes dominated by large changes in target rotational
angular momentum. In particular, the H$_2$($\nu=1, j=0$) total quenching cross
section computed using the BMP potential was found to be a factor of $~$1000
larger than that obtained with the MR surface.
