This review of the iPhone 5s is about what you’d expect. The author loves his new phone, points out things other reviewers have also raved about. But this bit focused on the difference with apps specifically compiled for the iPhone 5s’ 64-bit processor, vs their 32-bit iPhone 5 counterparts:

For instance, Night Sky 2 — it’s among those apps compiled in 64-bit — clearly gains speed during startup. It launches in 2.7 seconds on the iPhone 5S, compared to 4.6 seconds on an iPhone 5. Although 1.9 seconds may not sound like much, it’s still an indicator of the kinds of speed gains we’re likely to see as more apps are updated.

A better test of the new architecture is the new game Infinity Blade 3. For this quick test, I rebooted both devices and launched the game before running any other apps. From the moment I launched the game until the introduction animation ran, I found the iPhone 5S to be surprisingly faster than its predecessor. On first launch, the iPhone 5S needed 47 seconds to clear the loading screen and begin the animation, 14 seconds faster than the iPhone 5. For the second launch, I rebooted the phones again before launching the game. The iPhone 5S reloaded the game in 17.8 seconds compared to 48 seconds for iPhone 5. On the third attempt, the iPhone 5S needed 19.8 seconds, the iPhone 5, 37.9 seconds.

Those are some pretty significant differences.