In advance I should state that Im not qualified to give a definitive answer on the COP issue That said there are in principle two efficiency issues the first is the efficiency of a given enginetechnology the heat pump and the second the efficiency of a given systeminstallation the parallel for say cars may be identical engines using different gearing ratios or even tires In principle air conditioners and geothermal heat pumps use the same technology so the efficiency there shouldcould be identical in terms of work per unit of energy Geothermal pumps get their installed efficiency advantage compared to air source heat pumps ie air conditioners primarily from the fact that they are dumping the heat to a naturally cooler heat sink Or to put it a slightly different way an air conditioning system will be more efficient at an ambient air temperature of  degrees fahrenheit to cool to say  degrees than it will be at  degrees Since the ground temperature might be  degrees the ground source heat exchange system will cool more efficiently  dumping the heat is less costly and compressing a cold gas takes less energy than compressing a hot gas It can also work in a larger temperature range any heat pump will have a temperature beyond which it wont work well possibly at all  as the ambient temperature gets higher less cooling is possible I think there is actually a technical limit but this needs to be confirmed if the exchange medium cooling fluid expands at a heat level that is equal to or lower than the ambient temperature heat exchange may stop being possible or practical