I think the running costs are similar: the possible advantage of heat
pumps nationally/strategically is that the electricity they use can in
principle be sourced from non-fossil sources (if such are available)
whereas GCH is of course restricted to fossil-fuel (unless one acquires
renewable source of methane or similar).


My knowledge of these is not through practical experience of them,
but...

This is heat pumping, *not* geothermal heat.

This: http://en.wikipedia.org/wiki/GSHP#Thermal_efficiency

and everything else I've read about them says they deliver at least 3
times the heating efficiency of direct heating, *because* heat is
pumped.