I have the standard thin with a 1 11/16 nut and I love it. The fretboard is a bit wider than a Strat fretboard, so there's less string slip off. As for the neck contour, it is like a flatter, thinner version of a Strat neck contour. The most noticable differnece is how much less rounded it is; it looks more like the "D shape" neck from Philly Q's picture. So honestly I don't consider it similar to Strat C type necks, as they feel quite different from one another. In short, Standard Thin = thinner (from string side to back side), flatter, and wider (from one edge of fretboard to the other); Fender C Shape = rounder and narrower (from one edge of fretboard to the other).
(Just so you know, there are three modern Fender Strats in my house, in addition to my guitar with the Warmoth neck. I have also played quite a few Ibanez guitars. I guess all I'm getting at is that I have a pretty solid reference point and so hopefully I'm conveying the nature of the standard thin neck accurately)
One last thing I realized I forgot to mention: I have fairly large hands (more long than wide), but I've found that I'm most comfortable playing necks that are Femder C shape or thinner, rather than larger necks. So I don't think slimmer hands always need slimmer necks, or vice versa. Most people have large enough hands to play most electric guitar necks without excessive effort or struggling; the determing factor of which neck is most comfortable tends to be your playing technique and how you hold the neck.