A good test of his jaw strength might be to time how long it takes him to completely destroy a bully stick or shear the knot off of a rawhide bone.
Jack drops things while running all the time, and it's usually because he's bouncing around, mouthing the ball, or getting distracted. He does much better with sticks. That said, he's capable of puncturing a Jolly Egg so he can carry it, and does so with little effort--and that is some hard plastic. Ours destroys 6-inch bully sticks/rawhide knots in about 20 minutes when he's focused.