In brazing, the choice of base metal, brazing filler metal (BFM), and braze process conditions involves complex tradeoffs among cost, mechanical strength, corrosion resistance, and others. In this work, the tradeoff between strength and corrosion resistance of 316L stainless steel joints brazed with a newer “very corrosion-resistant” Ni-Cr-P-Mo-Si BFM and a more established “corrosion-resistant” Ni-Cr-Si-B BFM is quantitatively analyzed. Corrosion tests and microstructural analyses were performed using common practices. Joint strength was evaluated by testing brazed single-lap joints (SLJs) in tension following standardized procedures. However, conventional interpretations were found to be inadequate for quantitative comparisons. Therefore, the SLJ stress state was analyzed in detail and a complete interpretation was developed. Joint strength is shown to be determined by the SLJ geometry, base metal properties, and braze microstructure. This analysis was used to explain the occurrence of different failure modes (fast fracture, peeling, and base metal failure) and to make suggestions for improved methods for conducting and analyzing brazed SLJ tensile tests. The newer BFM is shown to provide significantly better corrosion resistance for a moderate reduction in mechanical strength.