I look terrible in visors and driving caps, and can't stand unstructured, so my vote would be structured.
Jconn, unstructed vs. structured
Unstructured (slouch)
vs
Structured
The unstructed hat is much more "relaxed" and softer. The front of the unstructured hat is not stiff like it is in a structured hat. The unstructured hats fit the top of the head better while the structured hats are designed to stick up.