The Spec C has more power than the Evo MR, at least in stock form. Both cars are rated at just '276hp,' but both make more than that. The Spec C has around 330hp, while I think the MR makes do with 285hp or so.
The Spec C may also be lighter, since it is a Type RA model. The RAs are pretty much rally-ready Imprezas with less amenities, kind of like an Evo RS. The Evo MR is available in lightened RS form, but only the GSR version appears in GT4.
For what it's worth, the six-speed RS version of the Evo MR was able to lap faster than the Spec C around Tsukuba in Best Motoring. Maybe lightening the MR GSR will help a bit in GT4.