While the differences in navigation and user ease when interacting or seeing a design are different, many of the ways to arrange content are often the same. Design elements such as shapes, lines, color and typography go into both digital and print design.
They both must also use the design space given for the graphic or information wisely. For print, they are many standard sizes such as letters, posters and business cards. But, printing surfaces can be cut to any shape and customized for specific needs. Web design can also tailor images to any dimension, but responsive designs that can easily be fit to appear normally on any device are more restrictive for online graphic designs.
A physical copy of the design excels by adding a tactile experience to the viewer experience. Your viewer can actually feel the texture of a print through effects such as embossing, letterpress and screenprinting. What competitive advantage web design has is the ability to incorporate interactive elements such as video and audio.
Consider a book. Many prefer having a physical copy because they like the feel of it in their hands. You can also easily highlight essential passages and truly see your progression as you turn the pages. E-books might not provide these benefits in the same way but have unique features such as useful hyperlinks or audio narration throughout the book.
When a physical design is final and ready for printing, any mistakes should be accounted for and corrected. Redesigning and printing costs money and consumes time. Web design can be edited at any time, even if it has already become final. A good example is a breaking news story, which expands with more information, photos and illustrations as more intel gathers. Prints require vast more certainty than digital designs.