As I understand it, "timestamp with timezone" is essentially a UTCTime plus a timezone. This would be useful when you're going to say something like "schedule a meeting for July 5 at 2pm, PST, and schedule another meeting every week at the same time." It's not sufficient to just take the UTCTime and add 7 days to it, because it needs to be adjusted for daylight savings time. "timestamp without timezone", on the other hand, is just the UTCTime.
Not sure if that clears things up at all. I know that I had a mistaken assumption about the distinction between these two types previously.