Yea, we do, but data you are putting out is based on the the antenna being mounted in a horizontal position. My modeling, based on the data in the ARRL Antenna Book agrees with the pattern and gain in said books when the dipole and EDZ are horizontal. If I switch both models to vertical, and put the EDZ's bottom at 20 feet off the earth, and the dipole at the same feed point height, you will be closer to a 2.2 dB difference between the two antennas. Move the dipole to the same tip height and the gain drops to 1.29 dB. Move the dipole's bottom to about 10 feet above the EDZ and it shows a gain of 0.47 dB over the dipole. Why the difference from the same antennas mounted horizontally? Vertical and Horizontal polarizations act differently, so you cannot take data from one and just assume it will be the same for the other.
Now factoring in AudioShockwave's point, as well as my own...
From there, in my case, take in to account that the bottom portion of my EDZ was below building level, and I got enough of a difference that my Starduster, which will have slightly less gain than a dipole, mounted about 10 feet higher than said EDZ, outperformed the EDZ in pretty much every way. Your environment and my environment were very different it seems.
If you are in a position that you don't have to worry about things like other buildings and hills and such, great. In my case, I didn't have that luxury.
But, as is shown when I raise the dipole comparison antenna higher the advantage in gain over that (and really any) antenna drops, and the EDZ will eventually be overtaken. The difficulties of raising any antenna beyond a certain point gets more and more difficult, and the EDZ gets to that point sooner than other free standing antennas. In the end I guess the question is how high can you mount the EDZ vs whatever other antenna you want to use. Also, how high are hills and structures in the area compared to said EDZ?
Even if you could raise the EDZ to said heights I think there is an effective upper limit in height to compete with other antennas for local contacts. Because of its directional nature, much like phased arrays used for some ham radio repeaters, at some point most of its signal will simply be over everyone's head, especially mobile antennas that are close to the ground.
Don't take this as me ragging on your antenna or idea. Far from it, I love the idea of a vertical EDZ, I simply have a different experience with said antenna. I have also thought about this antenna and its benefits and shortcomings in various situations in the past. I have also not seen any reputable sources refer to this antenna in its vertical form, and that includes ARRL publications, which makes some things harder. Unfortunately, you cannot simply take the horizontal information and comparisons of an antenna and assume they are the same for a vertical counterpart. It would be nice if we could, but it simply doesn't work... However, I will agree that it is about as good of an antenna you can get, in some very specific situations. I'm happy for you in that, as far as I can tell, you seem to be in one of those situations. The vertical EDZ is a worthy antenna for those who can take advantage of it. Unfortunately, I am not in a location where it will benefit me.
The DB