I use the browser addon for chrome and it looks like all the same features are on the desktop version that are present on the myibidder.com login settings also.

So I was wondering, under what type of scenarios do users use the desktop application rather than using the browser addon?

Everyone has their own needs. Your best bet is to try it and check it yourself.
If you don't find it useful at all, then it's not for you or maybe you just don't need it at that specific moment.