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Cost-wise, our house works out about the same either way.
Ours seems to be too. I turned the boiler down this year as an experiment, mainly to see if I could regulate the temperature a bit more effectively. When the boiler runs hot, the radiators get very hot, the room (air) temperature shoots up too high, thermostat clicks it off, temperature plummets, repeat. The temperature swings between too high and too low - and it's not particularly comfortable like that. With the boiler turned down, the radiators are nowhere near as hot, but they're heating the fabric of the house and not simply overheating the air in the room. The temperature is definitely more stable and it's far more comfortable.
Cost-wise, our house works out about the same either way. It's definitely more comfortable when on all the time as there's often someone home each day. Our graph looks similar to your first, with the different shades of grey showing how the boiler is modulating output to maintain a temp, rather than running flat out all the time.