I prefer the Edifiers. Both speakers do have their flaws, though.
The AV40's have pretty lackluster low end, and using the bass-boost just muddies the sound. The mids/highs are pretty decent, and perhaps slightly more detailed compared to the Edifiers. I have heard that these speakers have atrocious build quality, though.
The Edifiers bass at first can also be a little lackluster, but it does improve after some burn in period. I noticed they tend to have a mid-bass hump (exaggerated frequencies in the 120-250hz range approx) if you have the bass dial over 60-70%. Some people like this, as it tends to give it a "warmer" sound, but it can veil over some detail in the sound at times. If it bothers you, you can easily EQ it. The overall sound is great, though, and has much more weight compared to the AV40's.
Overall, to my ears, the AV40's are slightly more detailed but lack any punch... while the Edifiers are not as detailed, but sound fuller and more pleasurable to listen to.
If the Edifiers were the same price as the AV40's I'd still pick them.