What is the significance of characterizing a design application as a "continuation in part" versus a "continuation"?

Any drawings that were not present in the parent utility application will be considered "new matter," and any claims that rely upon new matter will get the priority date that such new matter was added.

This means that your design application will not enjoy the benefit of the non-provisional application's earlier filing date.  Instead, the priority date of your design application will be the date that the design application was filed.  You r design application could run into trouble if there were prior art references that were published after the date that your non-provisional application was filed, but before the date that your design application was filed.  Such references could have been completely avoided if you could have claimed your design application was a "continuation of" the  earlier filed non-provisional application, as opposed to a "continuation in part" of such an application.