Two of the main differences between the two are frame and engine power.
The difference in the frame is mainly due to ease of up-fitting beds and such. It is a lot harder to up-fit and cut into a fully boxed frame versus a c-channel frame. Not to mention that part of a fully boxed frame's strength comes form it being fully boxed so cutting into it may weaken it significantly. The c-channel frame may be thicker(and heavier), but that does not mean the fully boxed frame is not as strong. It is just easier to modify the c-channel frame which is why many many C&C trucks are fully boxed up front and c-channel in the back.
In regards to the power difference, this is due to emissions certifications. A complete pickup goes through what is called a chassis dyno certification since the truck is complete. This certification is less stringent and more power can be had. For C&C trucks, they go through a engine dyno certification since the truck is not complete when it leaves the factory. A lot of people think it has to do with duty cycles, but it is only due to different emissions requirements and certifications.
There might be a few other differences as well depending on the make and model.