I don't think anyone has really addressed the most important part of your question yet. There are a bunch of differences between compact digital cameras and digital SLRs. The most important one for action photographers is that digital SLRs have negligible shutter-lag. That means that the amount of time between the moment you press the shutter release and when the picture is taken is not noticeable. Compact digital cameras keep getting better, but I don't think any are close to any digital SLR yet when it comes to shutter-lag. And the fastest digital SLRs, the Canon EOS 1D, 1D Mark II, and the Nikon D2H, have absolutely no distinguishable lag. That means that the photographer and not the camera is the limitation when it comes to timing photos.
Another important difference between compact digitals and digital SLRs is the size of the sensor. Even though there are 6 megapixel compact digital cameras, the image quality won't compare to a 6 megapixel digital SLR. That's because the size of the sensor, and each individual pixel, is much larger in a digital SLR. Larger pixels means, cleaner, richer, sharper information. Even with the same number of pixels, digital SLR image files are much nicer-looking than any compact digital camera.