Associating schizophrenia with disrupted functional connectivity is a central idea in schizophrenia research. However, identifying neuroimaging-based features that can serve as reliable "statistical biomarkers" of the disease remains a challenging open problem. We argue that generalization accuracy and stability of candidate features ("biomarkers") must be used as additional criteria on top of standard significance tests in order to discover more robust biomarkers. Generalization accuracy refers to the utility of biomarkers for making predictions about individuals, for example discriminating between patients and controls, in novel datasets. Feature stability refers to the reproducibility of the candidate features across different datasets. Here, we extracted functional connectivity network features from fMRI data at both high-resolution (voxel-level) and a spatially down-sampled lower-resolution ("supervoxel" level). At the supervoxel level, we used whole-brain network links, while at the voxel level, due to the intractably large number of features, we sampled a subset of them. We compared statistical significance, stability and discriminative utility of both feature types in a multi-site fMRI dataset, composed of schizophrenia patients and healthy controls. For both feature types, a considerable fraction of features showed significant differences between the two groups. Also, both feature types were similarly stable across multiple data subsets. However, the whole-brain supervoxel functional connectivity features showed a higher cross-validation classification accuracy of 78.7% vs. 72.4% for the voxel-level features. Cross-site variability and heterogeneity in the patient samples in the multi-site FBIRN dataset made the task more challenging compared to single-site studies. The use of the above methodology in combination with the fully data-driven approach using the whole brain information have the potential to shed light on "biomarker discovery" in schizophrenia.