Mesh/subdiv modeling is a huge advance over NURBS because for the latter you needed to break down the object you planned to build into patches and then painfully create the edges of those patches, stitch them together, and so on. Just the explanation of how to connect two patches together without creating horrible folds (or to fix the folds you inevitably would get) was often dozens or hundreds of pages of unreadable crap.
With mesh/subdiv modeling what you do is much more intuitive and interactive. You build either (a) a small portion or (b) a crude approximation or (c) a crude approximation of a small portion of the object you are after and then work on it by progressive approximation and/or building out. But you still need to keep track of your topology to make it all work out nicely.
With volumetrics you're essentially working on a collection of "voxels" (little cubes) -- you can push, pull, scoop out, pile on the voxels and the program builds a topologically sound mesh around it to your chosen level of approximation on-the-fly. So, assuming you have a fast computer and good voxel manipulation tools, it is as much more intuitive than mesh/subdiv as that was over NURBS. And this applys particularly to surface detail ... if you're trying to put wrinkles on someone's skin, or warts on a frog, or chips in the teeth of a shark -- you don't want to have to think in terms of topology. (But if you're going to animate a figure, having full control over its high-level geometry is vital, so while volumetric modeling may be useful, an animated figure will end up being "retopologised" -- at least until it's possible to rebuild the mesh around the voxels, and animate the voxels.
The 2D equivalent would be like using MacPaint but having Illustrator autotrace your bitmap every time you did something and show you the autotracing as feedback instead of the underlying bitmap. (And consider how much more intuitive that is that learning how to use beziers (bezier curves are 2D cubic NURBs) or drawing a polygonal outline and then smoothing it (the mesh subdiv analog).
What C3D could really use would be better editing of subdived meshes. At the moment, when you edit a subdived mesh the feedback (e.g. which edge you have selected, and where that edge is) conforms to the original mesh, not the subdived mesh. (This is probably because this makes sense architecturally in C3D.)
In Silo 3D a mesh's subdiv level is an intrinsic property of every mesh, which means that Silo can show you feedback on the subdivided geometry -- which is huge. (Silo also lets you sculpt using zBrush/3DCoat/etc. -style displacement brushes, but that's a generation behind the volumetric modeling tools that are coming out now.)
Now, to do this in C3D would, presumably, be touch, since subdivision is a modifier. Of course it would be great if modeling feedback propagated through modifiers in all cases (e.g. the way it does in some very high end tools, like -- apparently -- Lightwave Core) or many cases (as in 3DS Max), but that's a tall order.