In this study a Computer-Aided Microscopy (CAM) system is proposed for investigating the importance of the histological criteria involved in diagnosing of cancers in microscopy in order to suggest the more informative features for discriminating low from high-grade brain tumours. Four families of criteria have been examined, involving the greylevel variations (i.e. texture), the morphology (i.e. roundness), the architecture (i.e. cellularity) and the overall tumour qualities (expert's ordinal scale). The proposed CAM system was constructed using a modified Seeded Region Growing algorithm for image segmentation, and the Probabilistic Neural Network classifier for image classification. The implementation was designed on a commercial Graphics Processing Unit card using parallel programming. The system's performance using textural, morphological, architectural and ordinal information was 90.8%, 87.0%, 81.2% and 88.9% respectively. Results indicate that nuclei texture is the most important family of features regarding the degree of malignancy, and, thus, may guide more accurate predictions for discriminating low from high grade gliomas. Considering that nuclei texture is almost impractical to be encoded by visual observation, the need to incorporate computer-aided diagnostic tools as second opinion in daily clinical practice of diagnosing rare brain tumours may be justified.