It's not impossible to get good action shots with a compact but it is more difficult, mainly I find because of shutter lag - the time that elapses between you pressing the shutter and the photo actually being taken - and as Hannah says the zoom doesn't tend to be long enough on them to get in close to the action. It's not just a matter of getting a DSLR and automatically getting amazing photos either though, they may be faster but you see just as many out of focus and poorly composed SLR photos as you do from compacts, and the lens you use definitely makes a big difference.