Lets get green.

To understand the differences, lets first understand how the two systems work. Air to water heatpumps work by heating a tank of water then circulating that warmed water around radiators in the home. Air to air works by heating coils and proactively circulating the room air through the coil. There is a variety of options for each room, wallmounts (as unit in blue picture), floor mount units (these are similar to conventional radiators, and ducted systems which are very discreet.

Air to water heat pump systems work by pumping a lower temperature around the radiators, typically half the temperature the radiators would be heated by a gas boiler so the radiators need to be upsized to work with a A2W (air to water) heat pump and possibly all radiator pipework - very intrusive and EXPENSIVE!  Then the system gradually builds up heat in the home over a few days. Unfortunately the climate in the UK isn't predicable so A2W heat pump systems arn't very responsive to UK sporadic weather.

Air to air heat pumps have the same efficiency as A2W but will heat a home around the same time it takes a gas boiler system to heat the home but using alot less energy. And with A2A systems - you also have cooling for the ever warming summer months! Comparing air to water against air to air is a no brainer!