The basic difference in the approach is that with SPIN Selling, you're focusing on leading your prospect to figure out for himself how what you're selling benefits his business situation. DC has the same approach, however it ALSO includes how to uncover a buyer's true motivation, which leads not only to the value for his business; but for himself.
While a fine difference, it could make a world of difference in application. You may be speaking to two different people in the same organization. With SPIN, you'll have the same sales approach for both. With DC, you could have different approaches for each decision-maker because they might each have different motiviations for making the purchase. For example, a young early decision-maker might be shown how recommending a purchase would put a feather in his cap come employee evaluation time... But a more senior person, say an owner or executive level person, might be shown how using your product or service will enable him to focus on more big-picture decisions, and therefore is worth its price.
The value is different to different people, and the DC method helps you determine that individual value and therefore buying motivation.