I have used a quad.
It is quieter on receive, less noise.
The quad allows you to hear weaker signals due to less noise.
The quad does seem to have less fading than a typical yagi, some say due to both polarization fields being on the quad where as the yagi has one or the other.
The quad does not produce any more notable gain than a similar yagi.
The Quad has less bandwidth than a yagi.
The quad is a mechanical beast and must be engineered from the ground up.
The quad has more wind load than a yagi.
With a quad it is not If it gets destroyed in bad weather but when.
I prefer quads, they are great for DX and local rag chews.
I use yagi's due to lighter weight and ease of construction.
I agree with every thing axcept most of it
the 3 el quad i had beat out the 5 el yagi in both recieve and transmit thats why i put it back up
it coverd more freqwencys than the yagi below 2to1 swr
its still working after 22 years withuot braking
it absorbed the wind much more than the yagi did because it would flax and give in the wind but the yagi didnt
it wieghed about one third of the yagi and its smaller
its only 9 feet wide and the yagi was almost 18