I'm a bit late in responding but I thought I would because I have a 14kW Ecodan. Mine is definitely oversized because my house will need nothing like 14kW most of the time. My ASHP can also deliver quite a bit more than 14kW if it has to. My house is a 160m2 bungalow with 13 radiators. I keep it at about 21C, running the ASHP 24/7. I don't use thermostats but control through weather compensation/flow temps only.
From the published data and my own observations my ASHP's minimum output is about 4kW. An 11.2kW model looks to be about 3.7kW or so minimum, so not that different.
In practice, this means that my ASHP cycles when it's warmer than about 7C ambient. The cycling is about three times per hour. Any colder out and it runs steadily. At its minimum steady running it's consuming about 1.2kW. I think I would have been OK with an 11.2kW model but I went with my supplier's advice and got the bigger one. As you said, the smaller model will be a bit cheaper, smaller and quieter.
Looking at the published data, it's clear that these ASHPs (and I assume others) are less efficient when working hard.
https://library.mitsubishielectric.co.uk/pdf/book/ATW_Databook_R32_2020#page-72-73
It's a bit fiddly but if you take a winter's day of 0C and assume yourvhouse will need say 9kW to heat it at 45C flow then you can compare the COP with the different models. I think what I'm seeing is that the bigger ASHP is providing its heat slightly more efficiently. I think also that the smaller model may have the edge at the lower end. If I had known what I know now I may have gone smaller but for me I don't think there is a lot in it. But if I were in any real doubt I would gone large.
Hope this helps.