I have both to 20 and 30 mm ligers with sapphire, sic, and obsidian.
The 20mm is great for small or tiny dabs however the insert will not hold enough heat to fully vaporize a larger one without increasing the temperature or waiting for the heater to catch up.
The 30mm inserts are a lot heavier so they hold more heat while providing more surface area. This size is far superior for medium-large- to gianormous dab. The only downside is that you have to suck a little harder before carb capping to keep the vapors in. Adding the August Haus coil provides more even heating and allows for even lower operating temperatures. Early reviews of the 30mm Liger were skewed as the first design did not always make tight contact between coil and vapor bucket however the designs was subsequently changed.
Quartz bangers are better than titanium alone as quartz holds a ton more energy per degree/gram as titanium which has a very low specific heat (but ok heat transfer rates). Quartz holds a lot more heat than titanium due to having a higher specific heat, however, it has the lowest heat transfer rates of all the inserts.
Sapphire has a higher heat transfer rate than titanium and holds twice as much heat per gram/degree as quartz due to having the industry's highest specific heat. Sapphire is also denser and has like 20x+ the heat transfer rate of quartz. This makes Sapphire an ideal concentrated thermal mass for rapid low-temperature static vaporization.
I see no reason why quartz would be better than titanium for housing the sapphire insert. The titanium wall that separates the CCA insert from the coil has a much greater heat transfer rate than a quartz banger. It is stronger, much thinner, and takes much less energy to heat up. This allows for quicker, more even, and more accurate coil heating and temperature readings. Furthermore, the coil heat shield on the CCA liger improves thermal efficiency while reducing infrared exposure.
If you are having issues with the 20mm liger than you are probably a heavy user who should step up to the 30mm rig. IMHO The 20mm liger is the ideal size for the lightweight/microdoser only.
I use the 20mm at around 660-670 on my China vapcode coil. I was running the 30mm a slightly cooler with my old flat coil. Now that I have upgraded to the 30mm August Haus coil and I am finding that I can use temperatures as low as 500-580. I'm not sure how accurate these numbers are.