Recent deep generative models (DGMs) such as generative adversarial networks (GANs) and diffusion probabilistic models (DPMs) have shown their impressive ability in generating high-fidelity photorealistic images. Although looking appealing to human eyes, training a model on purely synthetic images for downstream image processing tasks like image classification often results in an undesired performance drop compared to training on real data. Previous works have demonstrated that enhancing a real dataset with synthetic images from DGMs can be beneficial. However, the improvements were subjected to certain circumstances and yet were not comparable to adding the same number of real images. In this work, we propose a new taxonomy to describe factors contributing to this commonly observed phenomenon and investigate it on the popular CIFAR-10 dataset. We hypothesize that the Content Gap accounts for a large portion of the performance drop when using synthetic images from DGM and propose strategies to better utilize them in downstream tasks. Extensive experiments on multiple datasets showcase that our method outperforms baselines on downstream classification tasks both in case of training on synthetic only (Synthetic-to-Real) and training on a mix of real and synthetic data (Data Augmentation), particularly in the data-scarce scenario.