Is underfloor heating more efficient with stone flooring or parquet?

In advance, although we are currently building, I embarrassingly know very little about the technical features of our future house. Therefore, I cannot go into too much detail with my question. Our house will be very well insulated when it comes to thermal insulation. For heating, we have chosen an air-to-air heat pump and underfloor heating. We are now faced with the decision between oak parquet flooring or gres stone tiles in parquet look. From an efficiency standpoint, as far as I have understood, the stone floor makes more sense. We would be interested in the "feel-good experience." Is the stone floor unpleasantly cold compared to parquet floors during the time when it is not heated and with good insulation? We are also interested in whether the electricity savings due to better heat transfer are noticeable. I understand that this cannot be accurately determined without technical characteristics. I am only looking for a rough guideline. Is the difference around 10/20 percent, or is a bigger difference to be expected for a living area of approximately 150m2? Thanks in advance...

As heating, we decided on an air/air heat pump and underfloor heating.

You should explain that again. Because air/air means that the heat is transferred from air to air, which is exactly the opposite of underfloor heating. This would then be an air/water system.

Is the stone floor unpleasantly cold during times when it is not heated and with good insulation compared to parquet floors?

The surface temperature should correspond to the room temperature for both types of flooring. The tile still feels somewhat cooler. Do you walk barefoot? Imho negligible.

How does an air-to-air heat pump fit together with underfloor heating? Very well insulated is also quite a general statement. Otherwise, I can say about my underfloor heating that it is very subjective how one feels it. I usually wear socks, my wife and children are almost always barefoot, both on the stone tiles in our home and on the other floors. It doesn't get really warm even in winter; you only notice the difference when you step on the unheated stair steps. In terms of efficiency, there is no big difference when you consider how much screed mass is heated.

Yes, please explain the heating system again. Since nowadays heating is continuous 24/7 and well insulated towards the ground, the difference is just a few percent. Your supply temperature might be about 2 degrees higher with proper design. However, it is true that the stone floor always feels colder than the wooden floor.

Thank you for the quick answers. I naturally meant air/water.

We had the following in mind: if you walk barefoot or in socks in the house, then you need parquet because otherwise the floor with tiles is too cold on over 300 days a year.

If there are small children in the house, they fall more softly on parquet than on tiles... but parquet also gets marks quickly.

Savings on heating costs, if any, can only be marginal. Almost everyone here in the forum heats between 50 and 100 euros per month, depending on the size. You can neglect that.

We are happy with our wooden floor. You can get out all stains and with the marks, every new one hurts less than the previous ones.