Well, I decided to do a drop test with my brand, new Galaxy Note 3, since I had to break the screen anyways to do a future screen replacement video.
It turns out that the Samsung Galaxy Note 3 actually is pretty durable as the screen lived though a pocket drop, 5’9″ drop from the head, and even completely face-down drop from 5’9″. In the end, I did a near 7-foot drop, which was probably inevitable to expect not to break.
Overall, Note 3 is pretty sturdy phone even without a case I think but you should never expect your smartphone’s screen to live through these tests, I highly recommend you do use a case.