Been wanting to weigh in on this issue for a while...
There are an infinite number of factors that determine why one drop fares better for a phone than another drop - cases, protectors, angle, speed, distance, landing surface, and on and on.
I just recently put the Nano on my S4. Even if it's a false sense of security, it's worth it to me because I worry less about my screen and enjoy the phone more. But that's me. Everyone has different levels of anxiety about potential damage to their phones, real or perceived.
If you have 30 bucks to spare and you think it will give you more peace of mind, then go for it. No one here can assure you one way or the other since everyone's phone experiences and mindsets are different. Just know going in that nothing is a sure thing.
I've read enough posts on various boards saying that it's less about scratch resistance than about shatter protection. Some report from unfortunate drop experiences that the glass protector has shattered leaving the underlying original screen unharmed. Others say that's not typical. There's no definitive word on the subject, regardless of how authoritative some posters can sound. If there's a chance that I might avoid a shattered screen, then it's worth it to me. The Nano is pricey, but when I indulge, it tends to be on my techy stuff. Some might see that as foolish, but wouldn't hesitate to spend up on those bumper protectors for their cars, which I think is wasteful.
And, fwiw, you don't have to be a clumsy person to drop your phone. I never understood the argument that if you are careful with your phone, you shouldn't have to worry. Sh*t happens to the best of us.