OBJECTIVE: To quantitatively compare different spherical deconvolution (SD) approaches (ISRA-based and sparse L2L0 algorithms) to resolve crossing fiber in diffusion MRI. The purpose of this comparison is to address the area of application in which each approach could better perform. METHODS: Image Space Reconstruction Algorithm (ISRA)-based [Richardson-Lucy (RL), damped-RL] and sparse L2L0 algorithms were implemented and evaluated on both simulated data and in vivo datasets. Simulations were performed at different crossing angles (30°-90°), b-values (1000-3000 s/mm2), SNR (10-30), number of fibers (1-3). Isotropic compartments and different fiber volume fractions were included to obtain more realistic configurations. In vivo datasets were acquired to confirm simulated results. RESULTS: A decrease of SNR or b-value reduces the performances of both approaches. L2L0 methods have better performances at low crossing angles (30°-45°) whereas ISRA methods slightly prevail at high crossing angles (>70°). In the medium crossing angle range, the performance depends on the b-value. In the case of single and 3 fibers configurations as well as in complex scenarios (isotropic components, different partial volumes), ISRA algorithms were able to resolve fiber crossing more accurately and they outperform sparse L2L0 methods. In vivo results confirmed simulated trends. CONCLUSION: Both classes of algorithms can effectively resolve fiber crossing. L2L0 methods are more effective at low crossing angles whereas ISRA approaches have better performances at high angles and are more robust in more realistic configurations. SIGNIFICANCE: This work provides useful indications to select the best performing SD algorithm depending on the specific application.