One might think the plastic case on the iPhone 5c would make it more durable, but several tests have now shown that the 5s stands up much better. In fact, it even survives a drop of 10 feet when in Apple's new case. Android Authority was likely the first site to report a drop test, posting a video on the same day that the phones were first available.
In the video you can see that the phones were each dropped from chest height, first on their backs, then on their sides, and then on the front. The iPhone 5s survived all three drops, with only nicks to the casing. The iPhone 5c also showed nicks on the first two drops. But in the third drop, which tested the frontal impact, the screen shattered. The phone, however, would still turn on.
In the second video, posted by TechSmart, the two phones are dropped in turn from chest height, but in this test are housed by the cases that Apple introduced. The drop simulated the sort of accident you might have with the phone slipping out of your hand and falling on its edge. Both phones survived that drop in fine shape, with just little nicks to the cases. Then the phones were similarly dropped, but from a height of over 7 feet, again in the cases. The iPhone 5s again survived in fine shape, but the iPhone 5c was trashed. The screen shattered and the phone no longer worked. The next test was to drop the 5s on its face from a height of 10 feet. Again, no damage at all to the phone but there were nicks and slight tears in the case.
Finally, according to an article in the LA Times, in a durability test by SquareTrade of several phones that included dropping, submerging, and sliding off a table, the iPhone 5s outperformed the 5c. When dropped from five feet, the iPhone 5c screen shattered (but the phone continued to work), whereas the iPhone 5s only had a few scratches. Both phones survived the water test, continuing to play a video even after being dunked. In the the slide test, the iPhone 5s did the worst, sliding completely off the table.
Among the other phones the Samsung Galaxy S4 was completely trashed by the drop test, and didn't work after the water test. The Moto X performed the best among the four phones.