Hello Gene,
I would think, that it has more to do with the individual characteristics of the different woods, more than if they are stiff of not, if they are to be used as either backing or belly.
It has something to do with how the wood handles Compression (belly) and Tension (Backing). Either wood can be used - but each wood would require it's own bow-design, based on the woods caracteristics.
There are many posts that mention something about "this wood is good for backing", or "this wood is good for bellywood, but needs to be a wide design" or something like that.
Try search the different wood types in the forum, and see what other bowyers has used for either Back or Belly :-) ...
(I use primarily Ipé as Belly wood, and Bamboo as Backing. Also called a "BBI", short for Bamboo Backed Ipé)
Good hunting!