DSLRs have fundamentally different autofocus technology (phase-detection vs. contrast-detection), which radically speeds up the process of what happens when you press the button. With point-and-shoot cameras, you have to the whole half-press-wait-wait-focus-lock dance if you want to have low latency when you actually want to take the picture.

DSLRs also tend to be more willing to pipeline data from sensor to memory card, with bigger RAM buffers along the way. However, in the absolute newest generation of point-and-shoot cameras, the vendors seem to have decided that "fast response" is an important selling feature, so they're putting more effort into these very issues. It helps that Moore's Law has caught up with the processing needs of a compact camera. It also helps that the low end of the market has been obliterated by smartphones, so the only people buying point-and-shoots are the ones who want "quality" versus the ones who just want something that takes pictures.

(And don't get me started on how the 8 megapixel camera in my Droid X is notably worse than the 2 megapixel camera in my old iPhone 3G.)