This may well answer the question:

http://www.lithotherm-system.de/pdf/Lithotherm-English.pdf

Whereas when people talk of fast heat up in traditional UFH systems they are talking about self levelling compound etc and loose pipes directly under floor which while they heat up fast they also lose it quickly?

We have UFH in the bathroom mainly for barefoot comfort. It needs to come on quickly to warm the tiled floor at the time we want a shower, then be cold the rest of the day to reduce heat losses to the ground, the towel rad takes over the heating if needed. There is a layer of marmox insulation board to de couple the ufh+tiles from the slab.

This is example of low thermal mass construction where it is efficient to alter the temperature so it is 'just warm enough' at different times of the day. In other parts of the house we have a high thermal mass (same insulation layer but positioned outside the structure) and we have to keep the same temperature all day. Neither is necessarily more efficient, just horses for courses.

There are basically two ways to keep a temperature stable, keep the heat source close to the temperature you want, and then hold it there.
The other way is to let the temperature over and under shoot. The mean temperature will be the same.

So it is really just a matter of how much variation you want and how you want to achieve that.

You can, if you want, just limit the input temperature, but that may mean that it takes a long time to heat a room up. This is what happens when you have a large mass of concrete, or similar, to heat up before the rooms starts heating.

You basically have 4 variables, the power of the heat source, the time it takes to start transferring energy to the room, the mass of the air in the room and the desired temperature ranges.

Assuming that the heat losses are the same regardless of the type of heating, then you can either do short, high temperature inputs (like what radiators do) or you can, once the room is up to temperature, do small, lower temperature difference, inputs.
Both of those methods are controlled more by the temperature source i.e. gas boiler, heat pump, electrical resistance etc, than the amount of mass the heating system has.

Personally I think, and have no experience of comparing different types, that if you can control the flow temperatures reliably and within a small temperature range, it makes no difference, with the proviso that the floor is already up to temperature. Different matter if you want to use it like a traditional wet radiator system.

I am not totally sold on the idea that a high mass floor with underfloor helps when there is a sudden influx of energy i.e. sunlight.
The reason being that when the sun is high in the sky, it will not hit the floor, and when it is low in the sky, apart from having less energy (though still significant) the rays hit the walls.

Looking at their system from Lithotherm, it seems to be 0.0.45m thick and made from clay. Clay has a SHC of 0.92 kJ/(kg.K).
So that can hold around 0.013 kWh/(m^2.K) (assumption is that density is 1100kg/m^3).

Timber, with a SHC of 1.7 and a density of 800 kg/m^3 and still 0.045m (45mm) thick, has a thermal storage capacity of 0.017 kWh/(m^2.K)


So if you want to add mass, go for the clay tiles, if you want to add thermal storage, go for timber.

(I have not done an exhaustive search for all the possible SHCs and densities, but you get the idea and can do your own sums, and I have not double checked mine).

Faster heat up also allows for more variation in room temp from room to room e.g. cooler bedrooms, warmer living, and hot batroom.