As with most things care needs to taken in understanding the true benefits of these types of system. I'm making some generalisations here as technology changes all the time and what's below was true last time I looked.
Marketing likes to focus on the top level efficiency as provided by the Coefficient of Performance but in reality its the Seasonal Coefficient of Performance that provides a better indication. Efficiency in colder air temperatures tends to drop.
Also consider the needs of providing hot water and space heating.
Air to water systems can come in two flavours - low temperature of high temperature.
Low temperature systems are intended for underfloor heating and while they could be used with radiators, the radiators may have to be larger than a conventional system. Hot water tanks may also have to be larger and water temperature needs to be carefully considered to ensure high enough temperature to kill off Legionella bacteria - this may require an electric boost.
High temperature systems can be used more successfully with conventional radiators but the higher temperatures in the system usually result in a lower SCOP figure.
Consider also that conventional gas boilers can provide continuous instantaneous hot water whereas Air to Water systems that I'm aware of provide energy to either space heating or hot water, with hot water usually given priority. Once the tanks empty it will need to be fully heated to get more when you may only want small amount.
Consider also is the unit cost of the power source. According to some sources the price per kWh of electricity is 7.19p for an air source heat pump - and for a conventional gas boiler 4.16p, taking into account the efficiency of either system.
As a result the head line efficiency figure can be less than acheived in reality and the cost differential in fuel types may erode the savings further.
That's not to say that installing ASHP is a bad thing evironmentally but the cost impact to the end user needs careful assessment. Just like the cost of electric vehicles is putting off the adoption of them for some folks the potentially higher install cost of an 'gas boiler' equivalent ASHP system may put off installing this retrospectively. How long would the cost savings have to run for to pay back the difference in system cost? Hopefully before the system needs replacing.
New builds in the future, if the government gets its way, will have to have Heat Pump systems which may push up the cost of a new build. (Discussion of the noise of hundreds of condensers on an estate of new builds crammed together for another time - as is the surge in electricty as everyone comes home and turns the heating on at the same time as wanting to charge a couple of electric cars
)
In my opinion the issue of environment in respect of energy usage of homes needs addressing from at both ends of the problem. Not just coming up with more efficient ways of using more energy but better ways of using less.
Enough