Michelin Chef vs. Ordinary Housewife in their 40s: What if there's a difference in ingredients?

If we gave a Michelin chef a restriction to keep the ingredient cost under 7,000 KRW, and gave a housewife in her 40s unlimited freedom to choose ingredients, then assigned them both the mission to create the same menu, who would win?
Is the quality of ingredients more important in cooking? Or does culinary skill determine the outcome?