I know the thread is almost dead, but I have paid for both of the apps and tested them since WP7 times up to now and:
Weather Flow is "cheating" by not showing you really updated information. They pull data once for some hours in advance and then show it to you as current conditions, but very often the hourly forecast is not really accurate and I you see differences between the temperature in other apps and the "current" conditions in WF.
This is most probably made because they don't want to pay lots of money to WeatherUnderground for API requests and this way they make more money from their app.
By my opinion Amazing Weather HD doesn't look as good as Weather Flow, but at least they are providing us with accurate info.
Where Weather Underground data is concerned, a lot depends upon what station you're pulling that data from. Many of the personal (i.e. home hobbyist) weather stations will differ substantially from airport or government reported measurements. In my experience, this is especially true during periods where the equipment isn't getting hit by sunlight early or late in the day. So a personal station may be closer to your location, but not roof mounted or high enough to tell you what unshaded conditions are like during transitional periods. You wouldn't know this for certain unless you went and observed the equipment itself though. I do find the reported temperatures seem to normalize somewhat by midday or at night, which is consistent with that theory.
As far as the two applications are concerned, I do like the artistic elements of Weather Flow a bit better and I have no problems with updating that I can't trace to settings or OS limitations. However, it doesn't look at all like it's utilizing WU data. If I search my city by name, I get a bunch of results containing alternate weather stations, but those don't correspond at all with the PWS I see at Weather Underground's site.
With amazing Weather HD however, I can search for and pin locations just as they are described via WU's web site.