Low-dose CT (LDCT) imaging is widely used to reduce radiation exposure to mitigate high exposure side effects, but often suffers from noise and artifacts that affect diagnostic accuracy. To tackle this issue, deep learning models have been developed to enhance LDCT images. Various loss functions have been employed, including classical approaches such as Mean Square Error and adversarial losses, as well as customized loss functions (LFs) designed for specific architectures. Although these models achieve remarkable performance in terms of PSNR and SSIM, these metrics are limited in their ability to reflect perceptual quality, especially for medical images. In this paper, we focus on one of the most critical elements of DL-based architectures, namely the loss function. We conduct an objective analysis of the relevance of different loss-functions for LDCT image quality enhancement and their consistency with image quality metrics. Our findings reveal inconsistencies between LFs and quality metrics, and highlight the need of consideration of image quality metrics when developing a new loss function for image quality enhancement.