Deep image-based modeling has received a lot of attention in recent years. Sketch-based modeling in particular has gained popularity given the ubiquitous nature of touchscreen devices. In this paper, we (i) study and compare diverse single-image reconstruction methods on sketch input, comparing the different 3D shape representations: multi-view, voxel- and point-cloud-based, mesh-based and implicit ones; and (ii) analyze the main challenges and requirements of sketch-based modeling systems. We introduce the regression loss and provide two variants of its formulation for the two most promising 3D shape representations: point clouds and signed distance functions. We show that this loss can increase general reconstruction accuracy, and the view- and style-robustness of the reconstruction methods. Moreover, we demonstrate that this loss can benefit the disentanglement of latent space to view invariant and view-specific information, resulting in further improved performance. To address the figure-ground ambiguity typical for sparse freehand sketches, we propose a two-branch architecture that exploits sparse user labeling. We hope that our work will inform future research on sketch-based modeling.