AI-based data synthesis has seen rapid progress over the last several years and is increasingly recognized for its promise to enable privacy-respecting high-fidelity data sharing. This is reflected by the growing availability of both commercial and open-sourced software solutions for synthesizing private data. However, despite these recent advances, adequately evaluating the quality of generated synthetic datasets is still an open challenge. We aim to close this gap and introduce a novel holdout-based empirical assessment framework for quantifying the fidelity as well as the privacy risk of synthetic data solutions for mixed-type tabular data. Measuring fidelity is based on statistical distances of lower-dimensional marginal distributions, which provide a model-free and easy-to-communicate empirical metric for the representativeness of a synthetic dataset. Privacy risk is assessed by calculating the individual-level distances to closest record with respect to the training data. By showing that the synthetic samples are just as close to the training as to the holdout data, we yield strong evidence that the synthesizer indeed learned to generalize patterns and is independent of individual training records. We empirically demonstrate the presented framework for seven distinct synthetic data solutions across four mixed-type datasets and compare these then to traditional data perturbation techniques. Both a Python-based implementation of the proposed metrics and the demonstration study setup is made available open-source. The results highlight the need to systematically assess the fidelity just as well as the privacy of these emerging class of synthetic data generators.