There are several things that determine performance of a digital camera.

Shutter Lag - is the time between when you press the shutter button and the photo is actually captured. This is typically about 0.4 second. Most of this time is used up by the auto focus mechanism.
A few (very few) cameras have a shutter lag of only 0.1 second.
Long Zoom Lenses - usually have longer shutter lags.

Shot-to-Shot Time - is the time between single photos.

Continuous or Burst Modes - is a special mode that takes photos as fast as possible as you hold down the shutter button.

Flash Recycle Time - if you are using flash, the high voltage flash capacitor has to recharge between shots. This can take 2 to 3 seconds.

Low Light Situations (like photos indoors without flash) are a problem with any point and shoot camera. Because the shutter must remain open longer to gather enough light for a properly exposed photo. This leads to slow auto focus, and usually to blurred photos.

One of the cameras with the best performance is the Canon SD880IS.
Here is a link:

The DSLR cameras have a large amount of expensive high speed buffer memory, large batteries, and noise free ISO settings.
So they will outperform a point and shoot camera.