There is an ongoing debate on whether the message is superior to the design, or vice versa.
Art departments were common in all ad agencies from the 1940s onwards, which means design was thought of. But the highest ranking, and highest paid ad men were the copywriters. They would make the message, and then hand it over to the art department to fit the message with graphics. The art department's job was to FIT the design to the message.
This alone was enough for me to see that message was superior to design, at least back then. If one thing dictates the actions of the other, it would technically be superior.
When we bring it to today, design is still everywhere, and it is prominent in advertising, marketing and sales. But, again I ran across this principle of "fitting the design to the message". I took a look into a SaaS firm who had interesting color combinations, design choices, etc. When I looked further, their creative brief said they wanted the design to emulate "simplicity, usability, convenience, efficiency and effectiveness". That was their message, and they wanted the design to fit.
A great artist, let's take a painter, can craft the most beautiful piece and say "I wanted it to make you feel like ______". Again they want to get a message across with their designs.
You will often see designers and artists think of a feeling, mood or idea and then craft it into their art. Sometimes the reverse happens where they just make something, and then decide the message later. But, after speaking with many artist friends, they are still thinking with the message even when they don't think they are. They have a feeling, a mood, and then they create. Creation of art is rarely, if ever, not justified.
The greatest design makes you feel exactly how it intends. If the design conflicts with the message, then you have a failed campaign in the works.
The message precedes all design in the sales/marketing/ad world.
Art/graphics departments should not exaggerate the design just because they can, or to simply show off their skills. The most effective designs are the simplest. But they need to compliment and push forward the message.