We present a combined tomographic weak gravitational lensing analysis of the Kilo Degree Survey (KV450) and the Dark Energy Survey (DES-Y1). We homogenize the analysis of these two public cosmic shear datasets by adopting consistent priors and modeling of nonlinear scales, and determine new redshift distributions for DES-Y1 based on deep public spectroscopic surveys. Adopting these revised redshifts results in a 0.8σ reduction in the DES-inferred value for S​₈, which decreases to a 0.5σ reduction when including a systematic redshift calibration error model from mock DES data based on the MICE2 simulation. The combined KV450+DES-Y1 constraint on S₈ = 0.762_−0.024^+0.025 is in tension with the Planck 2018 constraint from the cosmic microwave background at the level of 2.5σ. This result highlights the importance of developing methods to provide accurate redshift calibration for current and future weak-lensing surveys.