There is a great article in a back issue (help me out here with which one guys) called 'A pair to draw to.'  The author builds a flatbow and longbow out of hickory and compares their performance.  The test is not perfect, but it does reveal the difference between the two styles when made from a white wood like hickory, ash, elm, etc.  You can pick up that back issue for about $3.
And, Dana I think there is a notable difference between the American flatbow and American versions of the longbow (i.e., the St. Charles semi-stacked style).  You are right to say that there is a more 'American' version of the longbow, but the flatbow is something different.  Typically, everything that is not a recurve or compound is called a longbow and this just adds to the confusion.  (Sorry to argue jots and tittles here  

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           J. D. Duff