The AF-S lenses have a motor in the lens body to make focusing much quicker, the AF lenses do not. If for instance you want to photograph a moving subject, such as a bird in flight, the autofocus on the AF-S lenses would maintain focus more consistently on the moving subject than most AF lenses. Also if you wanted to use a Teleconverter in the future to increase your focal length or zoom reach, the only Nikkor converters available now are not compatible with AF lenses, only AF-S (but not all AF-S lenses, you should check before purchase if this is a concern to you).
The speed of autofocus on each lens will differ, some AF lenses are quite fast, I have an old AF 80-200 which I've used many times for birds in flight. The autofocus on the 80-400 is notoriously slow, so with moving subjects you may not always get the photo you were hoping for as the AF system might not keep up. For stationary subjects though it is fine and the 80-400 is capable of producing good detailed images. As far as I'm aware there is only one version of the 80-400 which is the AF version. The AF-S version was never made but would be a great lens should it ever be made available.
Hope this helps, please ask more if not.