You have two orthogonal things there. I have both geothermal AND radiant heat so I guess I've got the best of both worlds. Radiant is very efficient because you're not heating the water much above ambient (my system runs between 90-120 degrees). It's also a very comfortable and quiet heat (no blowing air, warm toes, ...).
You can feed a radiant system from a water heater fired with a variety of fuels or with a heat pump.

Heat pumps efficiency is usually pretty good. The big issue with air sources is that whether it has enough capacity depends on your outside temperature. In colder climates you'll need some secondary source of heat (often the rather expensive resistive heat though other solutions are available). Geothermal doesn't have that problem usually. The ground water is always at a good 54 degrees or whatever. You can feed your heat pump to an air handler which is handy for cooling (which you can't really do with radiant). You can also use it like I do to raise the water temperature for the radiant heat.

Heat pumps typically also don't raise the air temperature much above the desired temperature for efficiency. This results in the "it's blowing cold air" complaint that people like my wife complain about with heat pumps.

Your best bet would be to sit down with a really knowledgeable contractor or engineer in your area to find out what makes the most sense for efficiency and comfort.

Good thoughts from Ron there. There are too many details to give one precedence over the other. Radiant floors might get the edge in heating applications but that depends on the fuel and proper amount of sub slab/edge of slab insulation at grade. The most important thing to point out is that radiant floors do not offer any cooling benefits while ground source heat pumps do.

I make the case in my radiant floor heating post that they are less comfortable and don't make as much sense in energy efficient homes. There is a similar case to be made for energy efficient homes with Ground source heat pumps (geothermal). These systems have high upfront costs. If you are building to current energy codes (2012 or 2015), then the simple payback of these expensive systems are questionable. When you build beyond these codes like with net-zero or PassiveHouse, then the energy requirements become tiny and you can efficiently heat your home with electric resistance, solar PV, or ductless air-source heat pumps.

If you are building a Mcmansion with average air-sealing and insulation with plans of long term ownership, then both systems can pay off quickly and be a good financial choice. I think most experts would advise you to first build an efficient building envelope. This strategy is usually the most cost effective path to energy efficiency, comfort and indoor air quality.

Thank you for the great advice