Applying Artificial Intelligence (AI) in the healthcare domain is getting benefitted day by day with the advancement of approaches, one of them being Bio-Signal analysis. In Bio-signals, efficient feature engineering and feature extraction (FE) is necessary for optimal results. Features can be extracted from different methods by Time, Frequency, and Time-frequency domains. Time-frequency domain features are the most advanced and perform well for most AI-based signal analysis problems. We introduced the application of Wavelet Scattering Transform (WST) to neuro-disorder classification and provided a comparative study with Continuous Wavelet Transform (CWT) and Discrete Wavelet Transform (DWT) for schizophrenia disease classification. We are one of the first to apply WST to EEG data for classifying neurological disorders. We have also extracted 12 statistical features from the data before sending them to classifiers for classification. We built six Machine Learning (ML) algorithms from two categories core/traditional ML (Logistic regression and Support vector machine) and Ensemble Learning (EL) (Decision Trees, Random Forest, AdaBoost, and Gradient Boost). In total we have conducted 18 experiments, our study found that ensembling methods performed better when features are extracted from CWT and DWT. At the same time, traditional ML methods performed better than EL methods when features are extracted from WST. Overall SVM performed better, but the best results are attained by Decision trees which are; 97.98%; 98.2%;97.72%; 95.94; values of accuracy, sensitivity, specificity, and Kappa score respectively, and execution time of 48.04 s; our proposed method performed better than the reported state-of-the-art methods.