We switched from oil to ASHP a year ago and it has saved us about £1k per year energy bills and loads of CO2.
House is 1800s granite 4bed, no gas, windy hilltop in Scotland, ongoing insulation campaign.

Who knows, we might also get RHI payments for it sometime (ok maybe not).

Ours is a 2-stage ASHP (two heat pumps in series) so it can deliver heat at 80C to run existing radiatiors without loss of CoP. No thermal store, but wish we had one, as then we could use offpeak electric, would then be even cheaper. Daikin Altherma HT. Inverter-driven 16kW. No electric backup heater. We retained the old oil boiler as backup, but have never needed it (even when -10C last winter)

The external box is identical to the aircon units that you see outside offices/shops, needs space in front and to sides for air flow (the fan really does blast air through it).

Downsides so far have been 1) noisy 2) expensive maintenance contract (condition of warranty).

Planning to get round to collecting/posting meter readings for first year, watch this space.