dSLRs and digicams are really two diff classes of equipment.
1. Larger format.
A dSLR sensor is many times the area of (i believe) all digicams, prosumer class notwithstanding. i don't think there are any digicam sensors out there even one quarter the size of a dSLR sensor. The Sony 828 sensor, at 8MPix, measures 8.8x6.6mm, against (say) a D30/D60/10D at 22x16mm - one sixth the area.
For technically superior prints, the larger the format, the better the pics. This was true in film; it is also true in the digital world.
Because for a given size print (say A3), the enlargement for a typical dSLR may be 20x. For a digicam, the enlargement is about 50x.
In other words, for an equal quality print, the digicam will need to demand (at least) 2 times the resolution from the lens, per unit sensor area. Digicam lenses are typically inferior to SLR lenses, or on par at best, they certainly do not resolve more than twice as well as SLR lenses, per unit image area.
A larger format also implies longer focal lengths for the same field of view, and shallower DOF. A 17mm/f2.0 on a digicam may claim 50mm equivalent, but a true 50/2.0 on a full-frame dSLR will blow it away in terms of quality and DOF control.
For those not concerned with large prints, this point is, of course, irrelevant.
2. Dynamic range - due to larger pixel size. The bigger a sensor pixel, the larger it's potential dynamic range. A 10D's pixel has about 4x the area of a digicam's, and a 1D's pixel about 9x. Also, a dSLR's pixels are uncharged until the mirror flips, unlike a digicam's which is already charged bcoz the sensor is being used to preview the shot. In other words, a dSLR get to use the full dynamic range of the pixels, while a digicam has to share what little it has between 'preview' and 'shoot'.
3. Regarding shutter lag and AF speed: actually this arguement not so valid.
Casio has some digicams actually having equal or faster shutter lag than some dSLRs; which means it can be done, and will be eventually by all digicam makers. Another reason is that the camera cannot 'click' until it has focussed - so the experienced 'shutter lag' may actually be a AF lag in disguise.
As for AF speed, i think the problem is the small lens. Even in the SLR world, bigger (faster f-stop) and better lenses usually focus faster, for the same SLR body, bcoz the camera needs subject contrast to focus. It's like a white-hair plucking contest with an old man and a 10 year old boy as subjects; the one plucking the old man's hair (SLR) will win, not necc bcoz he is faster, but bcoz he has so much raw material (contrast) to start with. i'm just guessing on this point though.
