Buy a house with electric heating? Or a new terraced house?

That makes no sense... the heating panels on the ceiling bother you, you confuse "expensive brand" with "good quality," etc. With those doubts, I would never buy the house...

But 1-2 troublemakers are enough whose quirks you have to experience daily to significantly reduce the quality of life

But that has very little to do with the type of house now. Besides, it nowhere says that the existing building stands in the middle of nowhere. It will also have its neighborhood, very likely a new development area given the year of construction. I had more peace in our terraced house than now with our immediate neighbors. I am in favor of the new building. 30 sqm more, you can create a quiet area if needed, if the open-plan room is not sufficient. And such a new kitchen and bathroom according to your own taste has very high appeal. Has the new building already been built or do you still have a say in the fittings as well as the wall placement?

What was the existing building heated with before these panels came?

I would probably prefer the existing house.
A reasonably large garden, which is likely already landscaped, means more free space around you.
Garage and therefore also storage space already available.
80,000 euros cheaper, for that I would check if anything can be changed with the heating.
Located outside, thus more quiet.

We have an air-to-air heat pump. So it’s no good.

It’s a Schwörerhaus.
The performance might be sufficient until September/October.
Then you would have to switch on the pce elements.

Because of the chimney, it’s okay though.
We see the air-to-air heat pump more as a dehumidifier in winter.
Otherwise, the upper floor would get too humid.

Additionally, we have installed IR panels.
That’s a completely different kind of heat, like a hot air blower (pce elements).

At some point, an air conditioner that can also heat will be added upstairs.

In other words, many roads lead to Rome.
I would take the Town & Country house and adapt it.

But you have already read that the new building would have 30m² more than the detached single-family house? 110m² would be way too little for me personally, even with the absolutely efficient, no-frills, optimized, thousand-times-built floor plan that Town & Country has. You always have to calculate the costs for 2 cars in cases like this, if you live outside the city but have to go somewhere daily due to lack of public transport... it should not be underestimated. In our old rented place, the tram practically stopped right in front of the door, now we live a few kilometers further, the bus has a terrible schedule. So a second car is needed. The 80,000 EUR more for the centrally located house are quickly saved again. And so on.