Why does calcium chloride cause a greater freezing point depression in water than magnesium chloride?
As quantified in Fig. 17 of Manual of Practice for An Effective Anti-Icing Program (FHWA-RD-95-202): 

By weight percent, MgCl2 depresses the freezing point of water to a greater degree than CaCl2, up to about 24%.  This is consistent with the freezing point depression formula, as Mg has less mass than Ca.  

Beyond 24%, CaCl2 is superior.  

This is because the eutectic point of MgCl2-water is at 21.6 percent, whereas the eutectic point of CaCl2-water is at 30%.  

The freezing point depression formula is only valid at reasonably low concentrations.  It is certainly not valid beyond the eutectic point.