That softness is critical. Not for the kids, but for the adults who have to clean up after them.
Stepping barefoot onto a Lego brick hurts, but stepping barefoot onto a Duplo brick is much worse. Those things look innocent enough, but in the dark they turn into veritable caltrops!
You think so? The Lego bricks have sharper edges and also I think that you put the same weight (of your body) on a comparatively larger area on the Duplos, so less pain. But, well, who am I to argue about your experience. (Never stepped on either of these in our living room although we had both systems).
They are probably partially compatible. With Duplo for example, it's easy enough to stack Duplo on top of regular LEGO bricks, but not the other way around. For stacking regular bricks on top of Duplo, you need to have bricks of the proper multiple in each dimension -- they need to be full height and a multiple of 2 in the other dimensions. The Quatro bricks are compatible in the same way -- you can easily stack them on top of Duplo or regular bricks, but not the other way around; You probably also need to do a transition layer from Quatro to Duplo to regular bricks.
I've seen people use Duplo and Quatro for space-filling when they needed a large amount of structural brick somewhere that won't be seen in the final model. Think having a LEGO city setup that has an underground level.
https://en.brickimedia.org/wiki/QUATRO