A tempered glass protector may shatter and save the screen - if the drop isn't too great - it's not designed for shock protection, but for scratch protection. (And they're inverse - the better the scratch resistance, the worse the shock resistance, and vice versa. A soft protector absorbs shock, a hard one won't scratch.)
What I've found to be the best combination is a case like the Otterbox or the Lifeproof, if they make one for your phone. I've had my phone in an Otterbox flung against a wall, dropped to a concrete floor face flat and other abuses, and nothing suffered, not the wall or floor, not the phone and not the case. (The silicone rubber protruding past the screen does the shock protection and the plastic screen cover does the scratch protection.) There are limits, of course. Fifty feet to concrete probably wouldn't do the phone any good. Nextel isn't making the i58 any more. (I've seen that one fall 12 stories and not show a scratch - after someone found the battery and battery cover.)