ᐅ Control the climate using underfloor heating or through the ventilation system?

300-600 euros depending on the design, plus the outdoor unit (also depending on the design between 800-2500), plus wiring and installation.

If you plan this early enough, the systems can also be installed centrally or integrated into the ceilings... otherwise, you have no choice but to use the common wall-mounted units.

Ceiling cassette units were once a topic for us, but I prefer to climate control the rooms individually. Besides, those units are not cheap...

A major advantage of wall-mounted units is that they allow affordable heating during transitional seasons – it works quickly and hardly costs anything (high COP values).

And nowadays, almost all manufacturers offer design models in their lineups.

Even during the transitional seasons, you hardly need to heat nowadays, only when it gets really cold. And then your ground source heat pump will definitely deliver high COP values. For me, the ground temperature is quite high after summer at least. An air-to-water heat pump certainly doesn’t perform any worse. And you don’t only heat the rooms where cooler temperatures are acceptable (bedrooms!).

Otherwise, I can understand the desire for air conditioning, but I decided against it because ->personally<- I don’t have any issues with "a few weeks of slightly warmer weather".

You don’t have to, but sometimes you just want it a little warmer for a short time – even in the bedroom.

Since underfloor heating is too slow to respond, an air-to-air heat pump for climate control is simply ideal.

The COP shouldn’t be compared to that of a ground-source heat pump; rather, it shows that these units can heat very efficiently.

I speak from experience, as in our last KFW55 apartment we definitely needed occasional heating and also had climate control installed.

However, it’s purely a nice-to-have feature. At first, I only wanted the pipes installed, but unfortunately, they have to protrude from the wall, which you wouldn’t want for a longer period.

This is probably similar to many (comfort) extras. Once you have experienced it, you want it again; if you don’t know it, you don’t miss it.
(And of course, user behavior regarding temperature plays a role). Since my parents’ house already had underfloor heating (so I am used to it), I have never experienced rapid temperature changes.