IARC cancer classification

After many years of sensational reporting about the cancer risks from Bayer’s Roundup weedkiller, with the main ingredient of glyphosate, it appears that the tide may be finally turning in the courtroom. When presented with complex science, juries understand it and get it right.
What chemicals, specifically, pose a danger as a potential human carcinogen? To address this issue two competing approaches, which use scientific data to evaluate chemicals for this danger, are at odds. Can we tease out which of these two may be “better”?