In my response below, I will assume the following:
* That by "C-print", you mean prints on color RA4 paper such as any of the Crystal Archive products (DPII, Maxima etc.) or something like (RIP) Kodak Endura, Royal etc.
* That by "Digital C-print", you mean that the RA4 paper is being exposed from a digital input (computer) using a modulated RGB laser or LED system and that the input is a digital file
* That by "traditional C-print", you mean that the RA4 paper is being exposed with an enlarger from a film (C41) negative.
* That the chemical processing, washing and drying of digital and traditional prints in your case is the same, or similar, and there are thus no influences of the digital/traditional choice on aspects such as print longevity etc. (which are mostly affected by sufficient blixing and washing, not by mode of exposure).
The main differences are:
1: With a digital C-print, it's generally easier to adjust the colors to taste. With optically enlarged prints from film, you have to rely on flashing, masking etc. On the other hand, optically enlarged C-prints give a certain color rendition "out of the box" that may be difficult to emulate when you're working from a digital (scanned) image and digital output onto RA4/AgX paper. It'll take some fidgeting with color adjustment curves to get what you want, and there's a chance you'll get close to what you get with optical enlargement, but not exactly the same.
2: When viewed under magnification, a digitally exposed C-print will show pixelation. Most digital exposure systems work at around 300dpi and even if properly calibrated, the individual pixels are visible when viewed with a (strong) magnifier. With the naked eye, it's very difficult or impossible to see this.