I'll try to tell you what I know. I can't cite any sources for you, this is stuff I picked up over the years. I learned quite a bit from some documentaries on the History Channel a few years back...
Every bow is essentially a big spring. The efficiency of that spring - its ability to store energy from the archer's draw and deliver it to the arrow - is what makes one bow better than another. If you have ever had the misfortune to shoot a warped bow then you'll know the whole bow vibrates with a loud "twang." That means some of the archer's energy is going into vibrational energy, not kinetic energy imparted to the arrow. That's bad.
If I recall correctly, European bows through the Renaissance all had a round cross-section like a staff. Modern wooden bows have a rectangular or diamond cross-section which for some reason is more efficient. No one had thought of that in the Middle Ages. This is an important point because medieval bows had less punch for their draw weight than do modern bows, even leaving out such modern improvements as fiberglass and pulley/cam systems (compound bows).
The short bow or self bow is basically just a round, tapered staff with a string. It's made out of some flexible wood which makes it rather springy. It's a fairly good weapon, and the easiest bow to make.
The long bow is always made out of yew wood. The staff is cut from near the middle of the tree so half of it is made of dense, stiff heart wood and the other half is light, springy sap wood. The dense wood is the part facing the archer. The dense wood resists being compressed and the springy wood wants to stretch back to its original shape. A properly cut yew staff is an efficient natural spring. It is more efficient than a standard bow and therefore is a better weapon.
A composite bow uses the same principle but instead of a naturally-occurring spring the bowyer makes an artificial one. The belly of the bow (facing the archer) may be made of wood or horn and the back is usually made of sinew laminated together with glue. My opinion is that this is a better spring than the yew-wood long bow. However, the proper manufacture of such a bow takes months or years, as multiple layers have to be carefully laminated, then thoroughly dried, with no cracking or separation. The glue used in the lamination is water-soluble so the whole thing is usually coated with resin and/or fish skin for waterproofing.
For a bow of the same size, I think a composite bow should at least equal the power of a long bow. However, composite bows historically were nowhere near the size of a long bow. In fact they were generally shorter than "short" bows. Composite bows were typically small enough that they could be fired from horseback, not something I would want to try with a European short bow let alone a longbow.
So if I were making composite bow stats for my own Saga, I would make them Expensive (since they take so long to make) and give them stats somewhere between a short bow and a long bow. And a Load lower than either.