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Originally Posted by fearn
Again, not quite. All things considered a bigger bow is desirable, because they tend to be more accurate and to throw bigger arrows. The English longbow and the older woodbows exemplified by the Eastern North American Indian bows are all examples of this, as are some African bows.
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Thing is, bows and arrows aren't simple. Their design takes into account the local environment, materials available, and intended use, and a lot of clever bowyers have independently come up with similar solutions for thousands of years.
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For some things, bigger bows are better. Sometimes bigger arrows are better. Not always! Consider Arab/Turkish sub-drawlength arrows used with arrow-guides, or the more extremely short Korean version, where the arrows were about 1/2 the draw length.
The English longbow is one of the bows optimised for maximum energy, which is very important for armour penetration. Most game animals don't wear armour, so not such a big deal for hunting bows.
Some of the stone/iron age European bows are large, probably moderate draw weight (i.e., pretty high draw weight for us moderns), and inefficient. Inefficient is a Bad Thing in modern archery, since it robs you of speed, and thus of flat trajectory. But if you're a hunter who has to make his own arrows, low velocity is not always a bad thing - it's easier to find you arrows when you miss.
For a self bow, starting from scratch, I find it's easier to make the bow than the arrows. Losing/breaking arrows is a largely ignored disadvantage of powerful and efficient bows.
As you say, it isn't simple. The optimisations for warfare, hunting, and sporting archery are all different. That's not even looking at the different types of warfare, hunting, and sport! We can add ritual archery to the list, too.