In advance, I should state that I'm 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 engine/technology (the heat pump), and the second the efficiency of a given system/installation (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 should/could be identical (in terms of work per unit of energy). Geothermal pumps get their installed efficiency advantage (compared to air source heat pumps, i.e. 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 70 degrees fahrenheit (to cool to, say, 65 degrees) than it will be at 110 degrees. Since the ground temperature might be 40-50 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 won't 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.   