Residential load profiles (RLPs) play an increasingly important role in the optimal operation and planning of distribution systems, particularly with the rising integration of low-carbon energy resources such as PV systems, electric vehicles, small-scale batteries, etc. Despite the prevalence of various data-driven models for generating consumption profiles, there is a lack of clear conclusions about their relative strengths and weaknesses. This study undertakes a comprehensive comparison of frequently used data-driven models in recent research, including Generative Adversarial Networks (GANs), Variational Autoencoders (VAE), Wasserstein GANs (WGAN), WGANs with Gradient Penalty (WGANGP), Gaussian Mixture Models (GMMs), and Gaussian Mixture Copulas (GMC). The presented comparison explores the effectiveness of the above-mentioned models on transformer- and consumer-level consumption profiles, as well as for different time resolutions (15-min, 30-min, and 60-min). The objective of this research is to elucidate the respective advantages and drawbacks of these models, thereby providing valuable insights for subsequent research in this field.