The Quad or "Loop" is a full wave, however it isn't a vertically linear full wave, but rather a "closed" circuit design, so it's a little different than having a full wave antenna that is straight vertical. Both sides of the coax are terminated into this antenna. Meaning, Half of the full wave's cycle is dedicated to the coax center conductor, and the 2nd out of phase half is connected to the sheid. There is also an "open" version of the loop as well, but the closed circuit is the most popular. The shape of the antenna elements curve to meet each other, so it doesn't act like a 36' full wave vertical antenna in that sense. A 36' vertical antenna technically has less gain than a smaller 22'6" 5/8 wave antenna. This is because, a halfwave is the longest you can keep an element's currents in phase, and once you exceed 5/8th wavelength, the out-of-phase currents start to cancel out enough to lose performance. Meaning even with a 5/8th wavelength antenna, 1/8th of the antenna is actually "out-of-phase". Once you get to a 3/4th wavelength, the out of phase portion starts to transition from being negligible to a degradation effect (loss) of antenna performance.
The exception of vertically lengthening for more gain, would be electrically phasing two antennas, in a way to cancel out the out of phase portion. This is known as Collinear antennas. Big Hair Antennas are the only CB antennas that I seen, that have done this. To make this work, you need about a 45' to 50' vertical antenna overall. Rumor is, he no longer making antennas though.
A quad on the other hand works a little more differently, and has a tad more gain than a dipole (2db theoretically). I am a big fan of Quads or full wave loops, because they also pick up less noise, and better matching solutions are available, than using the ol gamma match method (which has some loss).
i would like to see this big hair antenna with 50 ft of element. this is all very interestig and I hope to learn much from this.