Accurate liver vessel segmentation is of crucial importance for the clinical diagnosis and treatment of many hepatic diseases. Recent state-of-the-art methods for liver vessel reconstruction mostly utilize deep learning methods, namely, the U-Net model and its variants. However, to the best of our knowledge, no comparative evaluation has been proposed to compare these approaches in the liver vessel segmentation task. Moreover, most research works do not consider the liver volume segmentation as a preprocessing step, in order to keep only inner hepatic vessels, for Couinaud representation for instance. For these reasons, in this work, we propose using accurate Dense U-Net liver segmentation and conducting a comparison between 3D U-Net models inside the obtained volumes. More precisely, 3D U-Net, Dense U-Net, and MultiRes U-Net are pitted against each other in the vessel segmentation task on the IRCAD dataset. For each model, three alternative setups that allow adapting the selected CNN architectures to volumetric data are tested, namely, full 3D, slab-based, and box-based setups are considered. The results showed that the most accurate setup is the full 3D process, providing the highest Dice for most of the considered models. However, concerning the particular models, the slab-based MultiRes U-Net provided the best score. With our accurate vessel segmentations, several medical applications can be investigated, such as automatic and personalized Couinaud zoning of the liver.