While I agree that there is a link between the two, I believe that neither can prevail without first establishing a solid brand identity and branding strategy based on your core values. All good business decisions are made in alignment with the established brand. Your brand determines the position and strength of your entire marketing framework, and serves as a point of focus for your product(s). If you clearly and consistently brand your business and your product, you’ll have a laser-focused understanding of your business’s values and goals, and a self awareness that dictates all your actions (not just marketing) related to your product. Over time, you will build a stronger business identity.
Product is definitely more important! We've all learned marvelous ways to market nearly anything, but there needs to be the substance behind it in order for that marketing to end in successful sales of the product in the long run.
I agree with what Pete said. I think product and marketing are truly linked. I have a client with a very interesting product, but when we started, he had very little marketing, so, great as the product was, no one knew about it. Thus, he was not generating a lot of sales. So, you can't really have one without the other. When he got sales, customers gave feedback on product improvement. So, he tweaks his product when possible to cater to customer demand. In that instance, product improvement drives increased sales.
It depends on the business you're in. I've seen business with crap products do well with good marketing. In that case, their market doesn't need the best quality - or there are just a lack of better alternatives out there.
However, in competitive markets, a poor product will kill you. I've recently done brand + product work for two very competitive industries: fashion and financial services. In both cases, I've worked with companies with good products and companies with poor products. The companies with poor products were able to get traffic and leads (a result of marketing) but they were unable to convert once people saw the product or were unable to retain customers after they purchased.
The truth is that product IS marketing. Every interaction you have with a customer is an ongoing game of perception. Customers have infinite choice. They can - and do - leave at will. If your product - indeed their entire experience with you - doesn't meed their needs and desires, you'll lose them.
Product for sure. Marketing plays an important role during the launch. But when sales start coming in and your customer service or the product quality depreciates during that cycle, no amount of marketing will help. Good products and excellent humble customer service generates word-of-mouth publicity which is the strongest for of marketing.