I've used both the point-and-shoot coolpix as well as SLR cameras. I think there are two big advantages to the point and shoot cameras. First is that they are small, lightweight, and take excellent photographs when you can get the subject into focus and get the photo. Second is that they are moderately priced. The advantages of an SLR with a long lens is that generally speaking the autofocus feature is much more effective, and it is much easier to get onto moving or partly obscured subjects. In addition the image stabilization of newer long lenses is really helpful in hand-held situations. I'm a birder, and use photography to enhance my enjoyment of birding as well as to document my sightings. I have gone to an SLR camera essentially all the time because I was just not able to get onto birds fast enough and get focused often enough with the Coolpix.
A couple of hints on using the Coolpix. First get a fast high quality memory card. With a slower card it takes far too long to process each photo, making it essentially a one-photo or bust type tool. Second is to get a camera with a viewing sight so you don't have to rely on the viewing screen to find the subject. It is far faster, not a problem in bright light, and overall much easier to use. Good luck.