Garth -
That is a difficult question. As you know, wood "moves" with changes in temperature and humidity. Plywood sandwiches pieces of wood with the grain running in opposite directions. So when any given layer tries to move, it is prevented by the adjacent layers. This means it is more stable.
If you look at a solid wood door, it often has panels in it. Those panels float in a groove. If they were glued in place, when they expand and contract, they would tend to break the door frame. But since they are "floating," they can move without damaging the door.
So the more complicated the furniture is, the more you might benefit from a base of plywood and veneer over the top of it.
My guess is the furniture you are talking about is made from birch plywood, not solid birch hardwood. In that case, it could be more stable than anything built with solid wood.
If the veneering is done well, it should never be an issue. There is plenty of antique furniture built a century or more ago and the veneer is still firmly attached.
I think most people would feel that solid hardwood is the best. And some "purist" furniture designers look down upon furniture makers who use veneered plywood. But if the furniture is well made, I just don't see it as being an issue either way.
As for being able to tell if something is veneered or not, about the only thing you can do is look at the grain pattern on the edges or corners. If it is solid wood, you can see that the grain is continuous. If you see breaks in the grain patterns on edges or corners, you can assume you are looking at veneer.
- Jim
