He quoted word for word from Tom Rauch's post on your eham link. Tom Rauch is w8ji. A quote from his post in your link.
I'm guessing you were referring to someone else's test, however, Dick Whetstone, AD4U did make said claim, perhaps that is the specific part you were looking at in the link, and in the process completely ignoring what w8ji said?
When it comes to the w8ji link, you didn't link straight to the page with the relevant info, so I will do so...
http://w8ji.com/quad_cubical_quad.htm
On that page he shows a case where the quad outperform the dipole, and a case where the dipole outperforms the quad, unfortunately, the quad outperformed the dipole in the free space environment which actually doesn't exist on this planet. When he put those antennas over an earth the gain of the quad was actually 0.01 dB less than the yagi antenna's gain. However, in the same section he does mention that in some cases the quad can have up to (but almost always less than 1 dB in gain. How much of a difference does that make? You will never notice it, and neither will the people you talk to, it takes much more than that to be anywhere close to noticeable.
He goes on, so please read his page. On more than one occasion he states that a quad can have gain over a dipole, but in other situations it can also have loss as compared to a dipole. There is no definite backing on your claim for quads in general here.
Also from your antennex link...
Claims of superior performance does not specifically mean that the quad will have more gain, in fact later in the article it specifically states...
That doesn't sound to me like a him saying the quad had better performance...
I can go on here, but the short version is, while the quad has some benefits over the yagi, no one of repute is stating that it is superior to a yagi in all cases, and in some cases quads are inferior.
The DB
