I would think this has more to do with the quality of the camera and its output. If I find a crappy film point and shoot that doesn't allow me to claim all film cameras suck.
If I found that every one of the digital cameras I've purchased suck at taking the kinds of pictures I want then I would assume I suck at picking cameras. I would not assume that all digital cameras suck at taking pictures.
One of the biggest factors involved is going to be the quality of the lens. If the lens sucks then chances are you'll get bad pictures. A good film camera with horrible lenses will most likely get you bad photos.
Then, as you say, there's shutter speed to consider. Shutter speed will affect the resulting image based on the environment and situation where you are taking the picture. Most cameras meet the needs of most people, a cheap digital camera will not meet the needs of those who require high shutter speeds. Nor would a film camera. My question is, who cares? If it doesn't meet your needs then get a camera that does. For instance, get one that lets you adjust the f-stop.
Remember cheap, crappy film? That's the equivalent of a crappy digital camera. A cheap image sensor in a digital camera is roughly the equivalent of not only cheap film but a bad development of the film.
Technique is a factor as well. Hold your arms against your body and hold very still when you push the button, and then if possible also brace yourself against something solid, or better yet, brace the camera against something solid. In other words, keep the camera as still as possible when taking a picture, especially in low-light situations and/or use the flash. (In automatic mode) the cameras adjust their exposure times according to the amount of light.
