These are the kind of questions I had to struggle with to write my BRP steppe nomads supplement (to be published hopefuly some time, it is almost done). It is a rather complex question and I've read and heard so many things, often contradictory, that at last, I decided to make it simple. I think that trying to acurately simulate bows is a too complex thing. Not only the bow, its quality, the kind of arrows or the skill and strength of the archer, but also the use it has been made for (acurate firing, volley, mounted archery, life-time...) have to be taken into account. It is all about an optimal combination archer/bow/arrow/use/conditions. Almost every bow is the best for for of these combinations. My short experience in archery did not help much finding the magical formula.
You may have been trained with a coumpound bow, but if using it in stress or in movement during a battle or while trying to escape, it may not be much more efficient than a self bow, at least as long as acuracy is concerned. But for contests like for Ulysse or Robin Hood, where you have time to aim, a compound will surely help. Since the training of the archer is the first criteria, I'd not give a bonus but instead grant a higher basic score. Or may be only for aimed shots. If you play with the fatigue option, you may give some advantage as well. It would probably have no true advantage for instinctive shooting, which is actually what is understood under the Bow skill.
Such a bow would be seen as magical by primitive cultures with no understanding of mechanics, but has a kind of secret technics for high developped medieval cultures like the Chinese or the Muslims kingdoms.