Am using both right now, and they each have their own extra little advantages IMHO.
I love Weather Flow's back tile that displays if it's warmer, cooler, or 'about the same' as the previous day, along with advisory for if you should bring an umbrella or not - an easy "glance and go" weather monitor. I also love how the live tile displays the last time it was updated and the wind speed + chance of rain, as well as an icon that displays the kind of weather (i.e. partly cloudy), right on the front of the rich graphical medium tile. Edit: Forgot to mention how I like that Weather Flow's rich live tile displays the weather with "night" scenes and a dark sky when it is late, which is a nice bonus that isn't seen in Amazing Weather. Edit 2: After purchasing Amazing Weather, it now has night weather scenes in the live tile as well.
With Amazing Weather HD, I love all the different customization options for the live tiles, front and back. I also love that the hourly weather view actually shows hour by hour (rather than every 3 hours with Weather Flow) - there's a lot of detail for every hourly forecast, as well. The black metro theme for Amazing Weather looks really smooth and clean with good, detailed info (such as humidity) without being cluttered. You can even check radar/satellite and dig deeper for detailed textual weather descriptions for each day and an accompanying graph! I also really like the lockscreen images - they do seem to shuffle quite frequently though, wish I could slow it down. Oh yes, and Amazing Weather also has a "Feels Like" weather rating, which is good when factoring in wind chill and humidity - sometimes the difference between "Feels Like" and the actual temp is the difference between going out in pants or shorts for the day.
Out of both weather apps, Amazing Weather HD is *much* closer to the weather reported on my local news station (and also matches up fairly closely with Accuweather), whereas Weather Flow seems to generally be up to 5 degrees "off" at times... for my area, at least. Amazing Weather also loads MUCH faster. Hmm, reading all that I've just written, I think I'm going to have to buy Amazing Weather... I should have given it a more thorough comparison before I bought Weather Flow a couple months ago. Oh well.