I am curious which way I should go on the stringer. Foam or wood? Which is stronger and has better resistance to snapping?
Your stringer choice really depends on performance and style. 1/8" basswood stringers have been standard for decades and work really well. Our new HD foam stringers give the board more "pop" out of turns and are just as strong as the 1/8" basswood. The HD foam stringers also give you a choice of color and can be shaped with the same tools as used on the foam. No wood tools needed.
In the end, the snap resistance of a board really depends on the amount of fiberglass you put on the board. An all 4 oz glass board is much more susceptibe to breaking than a board with a mix of 6 oz and 4 oz glass or an all 6 oz glassed board (longboards or old school fish).