What is a sopisticated design? The dictionary defines it as "lacking natural simplicity ... complicated, elaborate." Some people say sophistication means elegance. The dictionary defines elegance as "tastful, refined and dignified in appearance or style". Complication alone can't make sophistication, but it does make things interesting. But if there is complexity and its a mess is that sophisticated? The mess is cleaned up through refinment. So refinement seems to be a key to sophistication too. Something refined is clear about the different parts, the dominate elements or parts and the relationships of all the parts to one another. So if something's complex and refined then maybe that means its sophisticated. Complexity is pretty easy to understand, its refinement that is the issue.
On its simplest level something refined has had all its parts analysed and addressed. In order to do that the stylist would have to break a visual situation down into its simplest parts and enumerate all the aspects of each of those parts and their relationships to the other parts. He'd then have to analyze those separate aspects and relationships and finally make judgements concerning adjustments to each separate issue.