I'd say that the bow wood(the physical characteristics) and bow length(in relation to the draw length) would determine whether wide and thin or narrow and thick should be used. Wood properties, ie. tension strong, compression strong or a combination of both fits in here too. IMO, osage, being both tension and compression strong can be used in almost any style common bows. It's only drawback would be physical weight. Hickory on the other hand is quite strong in tension but not so much in compression is more appropriate for a flat bow over an ELB style.
When in doubt start with a wide thin bow and adjust the style, the length, the width and the thickness accordingly as your experiments progress.