Tabular generative adversarial networks (TGAN) have recently emerged to cater to the need of synthesizing tabular data -- the most widely used data format. While synthetic tabular data offers the advantage of complying with privacy regulations, there still exists a risk of privacy leakage via inference attacks due to interpolating the properties of real data during training. Differential private (DP) training algorithms provide theoretical guarantees for training machine learning models by injecting statistical noise to prevent privacy leaks. However, the challenges of applying DP on TGAN are to determine the most optimal framework (i.e., PATE/DP-SGD) and neural network (i.e., Generator/Discriminator)to inject noise such that the data utility is well maintained under a given privacy guarantee. In this paper, we propose DTGAN, a novel conditional Wasserstein tabular GAN that comes in two variants DTGAN_G and DTGAN_D, for providing a detailed comparison of tabular GANs trained using DP-SGD for the generator vs discriminator, respectively. We elicit the privacy analysis associated with training the generator with complex loss functions (i.e., classification and information losses) needed for high quality tabular data synthesis. Additionally, we rigorously evaluate the theoretical privacy guarantees offered by DP empirically against membership and attribute inference attacks. Our results on 3 datasets show that the DP-SGD framework is superior to PATE and that a DP discriminator is more optimal for training convergence. Thus, we find (i) DTGAN_D is capable of maintaining the highest data utility across 4 ML models by up to 18% in terms of the average precision score for a strict privacy budget, epsilon = 1, as compared to the prior studies and (ii) DP effectively prevents privacy loss against inference attacks by restricting the success probability of membership attacks to be close to 50%.