You actually need both. There are pros and cons for both, but personally I prefer foam for several reasons. For the suit, make it entirely out of foam. As for the helmet, stick with pepakura.
1) Foam is easier and quicker compare to pepakura. In less than 2 weeks, I completed most of my kids Spartan 4 Warrior armor. However, it does take experiece working with foam. Check my tutorial video below to start.
2) No chemicals to deal with. All you need is hot glue gun. Once the armor is done, you seal the foam with Plasti-dip and paint.
3) Foam allows mobility. My kids wore their ODST armor (out of fiberglass). They could not move much in their suit. With foam, they could run.
4) Foam is much cheaper. 2 packs of EVA foam can run about $20-40, depends where you buy them. With fiberglass, you can easily spend $300 and above.
5) Foam is light and easy to strap together.
You can achieve the same level of detail using foam. Most people use EVA foam to make the big pieces. Foamies (or craft foam) is used to create the details. Foam armor can last a long time. It may require some repainting and maintenance after each wearing. Then again, that goes the same with fiberglass armor.
Here is the tutorial on my YouTube channel. It receives quite a lot of good reviews.
And here is the most recent pieces of Spartan 4 Warrior that I just completed. Still missing some details. You get the picture.