My 2 cents: Not a huge fan of MDF construction. The cuts never seem to be as smooth as I'd prefer. In this application, I'd personally prefer the smooth precut wood profile.

You could consider using the smail square dowel rods tacked to the back to give middle support. It's not the cleanest, but it could solve the support issue w/out the expense of the better hardwood. If cost is not an issue, then go the hardwood route.....as long as you stain it and not paint it.