Parkinson's disease (PD) is often associated with cognitive deficits, although their severity varies considerably between patients. Recently, we used voxel-based morphometry (VBM) to show that individual differences in gray matter (GM) volume relate to cognitive heterogeneity in PD. VBM does, however, not differentiate between cortical thickness (CTh) and surface area (SA), which might be independently affected in PD. We therefore re-analyzed our cohort using the surface-based method FreeSurfer, and investigated (i) CTh, SA, and (sub)cortical GM volume differences between 93 PD patients and 45 matched controls, and (ii) the relation between these structural measures and cognitive performance on six neuropsychological tasks within the PD group. We found cortical thinning in PD patients in the left pericalcarine gyrus, extending to cuneus, precuneus and lingual areas and left inferior parietal cortex, bilateral rostral middle frontal cortex, and right cuneus, and increased cortical surface area in the left pars triangularis. Within the PD group, we found negative correlations between (i) CTh of occipital areas and performance on a verbal memory task, (ii) SA and volume of the frontal cortex and visuospatial memory performance, and, (iii) volume of the right thalamus and scores on two verbal fluency tasks. Our primary findings illustrate that i) CTh and SA are differentially affected in PD, and ii) VBM and FreeSurfer yield non-overlapping results in an identical dataset. We argue that this discrepancy is due to technical differences and the subtlety of the PD-related structural changes.