The key difference between a digicam (aka fixed-lens camera) and a DSLR is the size of the sensor/lens (they go hand-in hand; a small sensor camera is usually equipped with a small diameter lens).
The inherent property of a small sensor/lens digicam is the depth-of-field that you get. Even an f/2.8 setting on a digicam can give you the equivalent of f/11 depth-of-field possible on a DSLR. This can be both advantageous and disadvantageous, depending on how you see it. An iPhone camera will give you great depth-of-field, making everything in the image sharp. This may be desirable sometimes. However, if you wish to shoot a shallow depth-of-field image of a flower, for example, you might find it quite impossible to do so.
The newly announced Olympus XZ-1 digicam with its cutting edge f/1.8 lens is alluring indeed. While this allows you to take great holiday snaps for keepsake, I would love to try it out for more seriously challenging shoots. At this point I honestly cannot say if I will be pleasantly surprised until I have put my theory to test.