That other thread is about dedicated GPS units and Phone apps, which are also GPS-based. A bike computer takes information from the bike itself - the wheels and crank, and does not have GPS. It usually has cadence, which neither GPS units nor phone apps have.

Starting out, one may be most interested in seeing speed, distance traveled, and cadence while one is riding, which computers are designed to indicate, as well as tracking mileage, averages from reset points and some other things. At some point, though, the data that a bike computer provides may not be as interesting as the data an app can present, which usually includes vertical, and is time/date stamped, sortable, etc.. The biggest difference, however, is that GPS units and apps relate to maps, which computers cannot. One could get a mount for a phone for ready display of an app that may be installed, but phones are not really designed to be mounted on bikes.