People were just talking about this: viewtopic.php?f=11&t=122956
They made a bigger deal out of this than it needs to be. Fatter necks give the impression that they are harder to play, it's not that, it's your individual hand size and mechanics. Just get what you like. Make some mental notes and then ask the person making your guitar if that sounds like something they can do. If you're getting something that's more of a stock guitar model, something all the dealers will take as trade level instrument, then just talk to the dealer. If they've had a few of them come through their shop they should be able to talk about details.
The nomenclature of description I relate to isn't C vs. D shape, but as you said it, from flat to curved, all neck profiles in modern guitars are basically some iteration of a D shape. And there are guitars with necks that feel like they have a small flatness in the middle of the back of the neck, and it can be annoying unless you like that kind of neck. Most necks are rounded entirely-
The thing about the concept of D vs. C is that it's highly subjective, not because D vs. C necks don't exist,but that guitarists can never agree upon a font style to use to standardize judgment over what constitutes a 'D' or a 'C' - Are we talking about a New Times Roman 'D' a Palatino 'C' or a Bold Arial 'D' ....
That's a graphic design joke..s0rry wrOng topic.