That is no longer the case technically. Single head splits have an equal (+ or - depending on brand and size) to Geo in all climates above around 0 - 5 deg F air temp. Below that equal loop temps must be above freezing to equal the same. Once you factor in duct loss and pumping costs you are at a lower efficiency. You also have the unmeasured and untested costs if the above ground temps most of the winter months are above freezing. The geo system has a habit of removing the heat from the ground and not being able to replenish it as fast over time.
If I were to go with geo I would have a giant house, spray foamed, with r30-40 walls, R60+ roof, conditioned crawl with 3lb+ roofing floor on the ground (since the ground will have a lower temp with geo you don't want it sucking the heat out of the house) and about or above a 4-5 ton load calc. Even then I would want a Mitsubishi or LG ductless VRF system that is ground sourced run on a phase converter and a variable speed loop pump. You would still be hard pressed if your design temp was above 0-5deg F to have a lower operational cost.
If you have a new duct system, inside the conditioned space, with supply and return wells with the required GPM that would be different. Otherwise, you are best to rely on technology and efficiency not available 10 years ago to pull the heat from the air as opposed to the earth.
Final example, the well pump I use runs on a 20amp breaker (although the operating amps are closer to 10) for 10 GPM. This will provide enough water for between a 2 to 5 ton system depending on who's math you use. My 9000btu system I am installing uses a 15amp breaker and 14guage romex. The only reason it doesn't use smaller is because there are no commercially available smaller breakers. A LG 2 ton VRF system uses a max of 10.2 amps running for heat. What does this mean? Well depending on your system, your loop (remember open loop is best case and closed loop requires higher flow rates with higher resistance) and temperatures, in many cases your water pump might use as much electricity or more than an entire ductless system alone for the same heat load. This makes the COP numbers completely unusable on a geo unit.
