Afterbangs are cheaper, meaning that cheaper materials are used. As a result the bases don't really hold wax all that well and the skis are slow-ish. Also they are symmetrical, so while great for park and skiing switch they are not good for carving on groomers.
Chronics cost more. They have a better base that holds wax (right? someone tell me if this is correct) and because of that they are faster (when waxed, of course. Wax your skis.) They are not symmetrical, so they will carve better when mounted a few cm's back from true center.
Also Afterbangs are softer. I would call them medium-soft whereas the Chronics are medium-stiff.
These are the main differences. I can't tell you which one is better for you, you're the one who has to make that choice.