We report on rate-dependent fracture energy measurements over three decades of steady crack velocities in alginate and gelatin hydrogels. We evidence that irrespective of gel thermoreversibility, thermally activated ``unzipping'' of the noncovalent cross-link zones results in slow crack propagation, prevailing against the toughening effect of viscous solvent drag during chain pull-out, which becomes efficient above a few mm s(-1). We extend a previous model [T. Baumberger , Nat. Mater. 5, 552 (2006)] to account for both mechanisms and estimate the microscopic unzipping rates.