Researchers have compared machine learning (ML) classifiers and discrete choice models (DCMs) in predicting travel behavior, but the generalizability of the findings is limited by the specifics of data, contexts, and authors' expertise. This study seeks to provide a generalizable empirical benchmark by comparing hundreds of ML and DCM classifiers in a highly structured manner. The experiments evaluate both prediction accuracy and computational cost by spanning four hyper-dimensions, including 105 ML and DCM classifiers from 12 model families, 3 datasets, 3 sample sizes, and 3 outputs. This experimental design leads to an immense number of 6,970 experiments, which are corroborated with a meta dataset of 136 experiment points from 35 previous studies. This study is hitherto the most comprehensive and almost exhaustive comparison of the classifiers for travel behavioral prediction. We found that the ensemble methods and deep neural networks achieve the highest predictive performance, but at a relatively high computational cost. Random forests are the most computationally efficient, balancing between prediction and computation. While discrete choice models offer accuracy with only 3-4 percentage points lower than the top ML classifiers, they have much longer computational time and become computationally impossible with large sample size, high input dimensions, or simulation-based estimation. The relative ranking of the ML and DCM classifiers is highly stable, while the absolute values of the prediction accuracy and computational time have large variations. Overall, this paper suggests using deep neural networks, model ensembles, and random forests as baseline models for future travel behavior prediction. For choice modeling, the DCM community should switch more attention from fitting models to improving computational efficiency, so that the DCMs can be widely adopted in the big data context.