It would be hard to convince me that you would ever want to display the price as the "option" when choosing shipping, the primary reason being that the "description" of the shipping option is always (in my experience), the unique identifier for the type of shipping that you are requesting.
If you consider the most common traits for shipping options, there are, generally, four:
- Shipping Option Description
- Delivery Time
- Delivery Agent (e.g., postal service, UPS, FedEx, etc.)
Looking at those attributes, only the Description (unless you have described them poorly) is ever going to be guaranteed to be unique . . . you could have multiple shipping options that end up being the same price, you could have multiple shipping options that would arrive at the same time, but are provided by different delivery agents, and you could have a single shipping agent that offers multiple delivery "speeds".
So, based on that, from a users perspective, the only trait that you could use for a single-attribute selection method . . . where you could guarantee that all of the options were unique" . . . would be the Description.