I was surprised to know that the composite-recurves actually have larger brace heights than the longbows.

If this is the case, then how is is that the composite-recurves have higher range and power than longbows of equal or slightly higher poundage?

Sure, a composite-recurve has greater efficiency, but it has a shorter powerstroke (higher brace height).
Doesn't these advantages and disadvantages cancel each other out?

Or is it that there is a different way to measure the powerstroke for a composite-recurve?

Not they do not necessarity have a shorter power stroke. Let us take my favorites for example, the varied and many horsebows. Their draw is actually quite long as these bows are MADE for either an eastern thumbring and draw OR the western styled three-finger draw. Draw lengths of 32-35 inches are not rare at all. Also, the reason, or at least the explaination as to why these bows store energy so efficiently(this is in laymans terms as I am no bowyer just an humble archer). The curves and recurves of these type of bows store and compound the energy during the draw giving you a much farther cast and faster arrow flight even at slower speeds. I love my horse bows. Either in your wood composites, fiberglass bows or even the really accurate (and expensive) horn bows being made today it is the curves and recurves of these bows that make them smooth on the draw and a pleasure to shoot. ALSO, it is recommended that for horseback archery you pick a bow thats draw is a bit less than what you are used to drawing. It isnt easy drawing a heavy weight bow from the back of a moving horse. If you want more info on this please go to www.spitfirehorsebows.com. Along with the products this gentleman sells(which I drool over yet cannot afford), he has a dearth of excellent information on HOW recurve bows function so well along with proper arrow weight as well a proper grain weight of arrow heads for optimal performance of your bows. I apllogise for being so wordy but i am a lifelong archer and it is one of my passions. I hope i have helped some at all!!!

Larger brace height? This might be true for types without set-back grips, but composite recurve bows with sharply set-back grips ("reflex" grips in modern bow marketing terminology, though I disapprove of the confusion this might cause with the other kind of reflex) often have fairly low "brace heights" if by this we mean the distance between grip and string when the bow is strung but not drawn. In fact, the set-back grip appears to be designed specifically to increase the length of the draw stroke within a given amount of draw length, and it appears to work fairly well for that purpose.

Other mistakes that I need to correct are the myths that "composite-recurves have higher range and power than longbows of equal or slightly higher poundage" and "composite-recurve has greater efficiency." Archery equipment design involves a really complex calculus between the properties of the bow, the arrow, and of the archer; and while there are (obviously) situations where a static-recurve composite horsebow is more efficient than a medieval English longbow, there are also situations where the reverse is true.