The main benefit is that air to water systems are compatible with existing central heating systems - but only if the radiators are sized correctly, and often they're not.

If you factor in the need to replace radiators etc, then the ability to act as an air con probably makes air to air the better choice. Now that the Boiler Upgrade Scheme grants cover air to air as well as air to water, I'd expect them to become much more common in the UK than they have been until now.

The top end of the range they've shown here for A2W will assume you only heat the water to a very low temperature, and have a huge underfloor radiator. If you do that, and you only heat the water to 35C, A2W can be more efficient.

Most UK houses have radiators and not underfloor heating and so cannot operate in that way without a hugely expensive retrofit of underfloor heating. It's typical to heat the water to over 50C if you want to reuse installed radiators. In this configuration the A2W pump is less efficient than A2A.

Worth noting these numbers are low. Latest A2A pumps can have COP of up to 4, but an A2W can achieve 4.5 if you keep water temps very low.