The composite bow is one made of various elements, thus its name.
It is possible to make a composite bow with the pull of a longbow. But then the following rule would have to be amended:
If you have a Strength bonus, you can apply it to damage rolls when you use a composite longbow (see below), but not when you use a regular longbow."
It makes no sense to apply the strength bonus to one and not to the other when both have the same draw-weight. After all they have practically the same range and damage. It's just the build that changes and how compact it can be. Allowing the composite bow to be used while mounted.
BTW, shouldn't higher strength mean longer range? After all it means the character can pull a much stronger bow, right?
Source http://www.d20pfsrd.com/equipment---final/weapons "composite longbow"