The Human collections are generally more comprehensive than the Mouse collections, however if you are interested in the more "canonical" collections like GO, Reactome, etc. I'd probably recommend doing the analysis in the native mouse-gene space.
The specific gene ID type doesn't really matter, we offer CHIP files for both analysis in the native gene-space, and for ortholog mapping to the cross-species analysis.
-Anthony
Anthony S. Castanza, PhD
Curator, Molecular Signatures Database
Mesirov Lab, Department of Medicine
University of California, San Diego