We carried out first-principles calculations to simulate Ag2ZnSnS4 and Ag2CdSnS4 and calculated enthalpies of different plausible structural models (kesterite-type, stannite-type, wurtzkesterite-type, wurtzstannite-type, and GeSb-type) to identify low- and high-pressure phases. For Ag2ZnSnS4, we predict the following transition: kesterite-type→[8.2GPa]→ GeSb-type. At the transition pressure, the electronic structure changes from semiconducting to metallic. For Ag2CdSnS4, we cannot decide which of the experimentally observed structures (kesterite-type or wurtzkesterite-type) is the ground-state structure because their energy difference is too small. At 4.7 GPa, however, we predict a transition to the GeSb-type structure with metallic character for both structures. Regarding the sensitivity of the material to disorder, a major drawback for solar cell applications, Ag2CdSnS4 behaves similar to Cu2ZnSnS4, both showing a high tendency to cationic disorder. In contrast, the disordered structures in Ag2ZnSnS4 are much higher in energy, and therefore, the material is less affected by disorder.