Texture segmentation constitutes a central task in image processing, classically based on two-step procedures consisting first in computing hand-crafted features devised from a priori expert knowledge and second in combining them into clustering algorithms. Deep learning approaches can be seen as merging these two steps into a single one with both discovering features and performing segmentation. Using fractal textures, often seen as relevant models in real-world applications, the present work compares a recently devised texture segmentation algorithm incorporating expert-driven scale-free features estimation into a Joint TV optimization framework against convolutional neural network architectures. From realistic synthetic textures, comparisons are drawn not only for segmentation performance, but also with respect to computational costs, architecture complexities and robustness against departures between training and testing datasets.