Form - Foam: Soft, flexible, and foldable like cloth.
Pepakura: Hard, resistant, and feels like ARMOR.
Fit - Foam: Made to fit personal form
Pepakura: Made by modeler. Will only fit perfectly if model is modified, made by yourself, or just by chance coincidence.
Functionality – Foam: Action gaming such as Nerf battles. (running, dodging, and any other quick movements)
Pepakura: Conventions (standing around looking cool). Movie quality look. Or on display.
Weight - Foam: Includes foam, glue, and accessories.
Pepakura: Includes paper, resin, fiberglass mat, bondo (as needed)
Difficulty – Foam: Depends on experience
Pepakura: Depends on experience
Cost – Foam: Depends on supplier
Pepakura: Depends on suppliers, technique, and details
Versatility - Foam: Each is made specifically for one person. One piece at a time using trial and error (unless using template).
Pepakura: Can be easily replicated using any molding process or vacuform. Molding process mostly used by people trying to sell multiple copies or to have the finished product lightweight. That in turn can make it weaker and more brittle.
Ultimately you need to decide what it will be used for, your budget, your patience, and your skills. Your time dedicated to the project will ultimately be a calculation of all the fore mentioned requirements.