Recycling rare-earth elements (REEs) from Nd-Fe-B magnet waste is an important step towards building a sustainable REE supply chain. In this study, two different processes were systematically investigated and compared. In the leaching stage, the effect of increasing H2SO4 or HCl concentrations were studied and it was determined that, although both can successfully promote REEs, B, Fe and Co leaching, HCl solutions extracted a wider range of metals. After leaching, the oxalate and double-sulfate precipitation methods were utilized to separate REEs from either HCl or H2SO4 leachates. Results suggest that, although > 99% REEs precipitation rates could be achieved with oxalate, the purity of REE-containing products is significantly affected by impurities like Fe and Co. In contrast, REE double-sulfate precipitation resulted in a product purity of > 99%; however, high levels of Na2SO4 (8 times the stoichiometric amount) were needed to achieve > 98% of REE precipitation.