This is an interesting question and is an area I have spent a lot of time studying over the last several years. The best possible performance of a bow depends on the the mechanical properties of the materials used to make the bow, and string. It also depends on the testing parameters that the bow is judged against. It turns out that a bow made of suitable bow wood uses the nearly the full potential of the wood it is made out of to provide the structure, and energy storage capacity for a decent 40-50 pound bow drawn to 26-28 inches. This coincides pretty well with the needs of many archers. With a modern low-stretch string, an optimal all-wood now can keep up pretty well with modern composite designs.
For the same draw length and draw weight, modern glass composite designs typically don’t even come remotely close to taking full advantage of the energy storage and structural properties of the glass for a typical 50 pound draw weight at 28” draw length. In order to achieve to push glass as close to its limits as the wood bow, the bow would need to be made so narrow, and so thick, that it will not have enough lateral stability to even function. It will just end up bending sideways. So these glass bows end up much heavier than they theoretically should be.
In contrast, glass is really capable of producing some mind blowing performance when the design of the bow is optimized to take full advantage of its properties. For example, crossbow limbs in excess of 300 pounds of draw weight, and short draw lengths which are capable of sending a hunting weight arrow downrange at 400 fps. These bows are not one shot wonders either. They even carry a manufacturers warranty and these will wear out the one shooting them before the bow limbs give out. A wood bow designed to the same extremely heavy draw weight and shortish draw length would have to be built with such wide and long limbs, that it couldn’t come close to the same level of performance.
Horn and sinew composites are in a similar bucket as the glass bows. If the draw weight is low-to-moderate, and draw length is long, then they don’t perform much better than an all-wood bow. But heavy draw weight designs take much better advantage of the materials and performance really starts to shine.
Carbon fiber is its own unique animal. It depends on how the carbon is configured. Unidirectional carbon has superior structural performance to glass, but it is inferior at storing strain energy. This forces carbon designs to have more working limb than a glass bow. A typical 50 pound at 28” draw bow made with unidirectional carbon is also pushed closer to its material limits compared to a typical glass bow designed to the same draw length and draw weight parameters.
There’s much more to it, but this covers it at a high level.
Alan