Machine learning approaches are increasingly suggested as tools to improve prediction of clinical outcomes. We aimed to identify when machine learning methods perform better than a classical learning method. We hereto examined the impact of the data-generating process on the relative predictive accuracy of six machine and statistical learning methods: bagged classification trees, stochastic gradient boosting machines using trees as the base learners, random forests, the lasso, ridge regression, and unpenalized logistic regression. We performed simulations in two large cardiovascular datasets which each comprised an independent derivation and validation sample collected from temporally distinct periods: patients hospitalized with acute myocardial infarction (AMI, n = 9484 vs. n = 7000) and patients hospitalized with congestive heart failure (CHF, n = 8240 vs. n = 7608). We used six data-generating processes based on each of the six learning methods to simulate outcomes in the derivation and validation samples based on 33 and 28 predictors in the AMI and CHF data sets, respectively. We applied six prediction methods in each of the simulated derivation samples and evaluated performance in the simulated validation samples according to c-statistic, generalized R², Brier score, and calibration. While no method had uniformly superior performance across all six data-generating process and eight performance metrics, (un)penalized logistic regression and boosted trees tended to have superior performance to the other methods across a range of data-generating processes and performance metrics. This study confirms that classical statistical learning methods perform well in low-dimensional settings with large data sets.