Chemical reaction between dichloromethane and solid carbon dioxide
In brine cooling happens only on the surface of the solid carbon dioxide and causes the water to freeze there, forming an insulating layer (the same happens with ethylene glycol). In dichloromethane, which freezes below $-97$ degrees, no freezing occurs. Moreover, carbon dioxide is well soluble in dichloromethane, which makes the heat transfer more efficient. The latter property may cause you problems if you want to use your coolant in closed installations, because after warming the solution may release the excess of carbon dioxide.