In the last few days of usage, TouchID crashed once. It didn't accept my trained fingerprint, but wouldn't deny my untrained fingerprints either. It just didn't work. This seems like a software bug. iOS 7, esp. on the iPhone 5s, is still rough around the edges. Case in point:
Battery life has been decent though. I got the phone on Friday, recharged it that night, and then used it lightly to moderately until the battery died 2 days later.
Safari is lightning fast on this 5S. Pages pop up instantaneously and a couple of times I was waiting because nothing was happening, only because it had already happened. The page loading was so fast that I didn't see it. On my previous phone (RAZR HD), I could always watch it load up.
However, the speed for rendering really depends on Safari, as everyone knows. Chrome seems noticeably slower in some stuff, and that difference is illustrated by some (limited) benchmarks. Safari is much, much faster on iOS than Chrome.
SunSpider 1.0.1 Safari: 420 ms
SunSpider 1.0.1 Chrome: 1477 ms
In this JS bench, Safari is 3.5X as fast as Chrome.
As for Peacekeeper, Chrome on my 5S gets 1107, but Safari gets 1718:
The camera is truly a big improvement. Not only is the low light quality better, but everything they said about the more consistent colour balance and exposure settings is absolutely true. For example, I used it to take a video of a birthday party, when the candlelit cake was coming out. The room was completely dark and the only lighting was from the candles. The iPhone 5S correctly chose to keep the exposure very dark, only allowing the faces lit by the candle to be seen. The flash is also quite accurate for skin tones. This was taken in near-complete darkness. I just held my hand out in front of the phone and pressed the shutter release button. The camera did a pre-flash, and then snapped the flash picture:
My hand is the right colour, as are the beige blanket and my white shirt.