Research into machine learning methods for fraud detection is of paramount importance, largely due to the substantial financial implications associated with fraudulent activities. Our investigation is centered around the Credit Card Fraud Dataset and the Medicare Part D dataset, both of which are highly imbalanced. The Credit Card Fraud Detection Dataset is large data and contains actual transactional content, which makes it an ideal benchmark for credit card fraud detection. The Medicare Part D dataset is big data, providing researchers the opportunity to examine national trends and patterns related to prescription drug usage and expenditures. This paper presents a detailed comparison of One-Class Classification (OCC) and binary classification algorithms, utilizing eight distinct classifiers. OCC is a more appealing option, since collecting a second label for binary classification can be very expensive and not possible to obtain within a reasonable time frame. We evaluate our models based on two key metrics: the Area Under the Precision-Recall Curve (AUPRC)) and the Area Under the Receiver Operating Characteristic Curve (AUC). Our results show that binary classification consistently outperforms OCC in detecting fraud within both datasets. In addition, we found that CatBoost is the most performant among the classifiers tested. Moreover, we contribute novel results by being the first to publish a performance comparison of OCC and binary classification specifically for fraud detection in the Credit Card Fraud and Medicare Part D datasets.