I went back to check on the manufacturer of my second stone (not the Fibrament) and it is sold under the name Old Stone. I also double checked the thickness, and it is about 1" overall but that includes what look like "feet" or pedestals on the bottom. The Fibrament stone has no such pedestals, and its thickness looks to be a tad less than 3/4". I have not been able to detect any significant differences in performance between the Fibrament stone and the Old Stone stone.
Other materials that you will find for pizza stones are cordierite, a blend of compressed earthen materials, and soapstone, a natural mineral product quarried like marble and granite. The HearthKit unit that is sold for baking purposes is made of cordierite. You will find many sources for cordierite stones, and my recollection is that they cost a bit less than the Fibrament stones of equal size.
Soapstone is harder to find for home pizza baking applications, although All-Clad, the high-end cookware company, sells soapstone cookware in metal holders. They are very expensive for the sizes of the soapstone inserts (around $100 for a small stone unit). It is possible to go to a soapstone company, like those that process soapstone for home use (countertops, flooring, etc.), but it is very expensive to do this. Out of curiosity, I called Vermont Soapstone, in VT. (the state that supplies most of the soapstone in the U.S.), and was quoted a price of $77 per square foot, plus shipping. If my math is right, for a 16-inch square piece of soapstone, or a 1.3 ft. by 1.3 ft. square piece, the price would be around $137, plus shipping.
I suspect that there is a way of determining which of the many types of stones is best for use in baking pizzas in a home oven. To know for sure, you would need access to heat capacity characteristics of the different materials for comparably sized stones. It would most likely be the one with the highest heat capacity, that is, the one that retains its heat the longest (and cools down the slowest). Mass, which is related to thickness, is also a factor. A large mass will take longer to heat up to a particular temperature, but will also cool down the slowest. This characteristic is especially important if you plan to make several pizzas at about the same time, where you will be opening and closing the oven door a lot. In those situations, you want to have a stone that will retain its heat for as long as possible.