I haven't really noticed a speed difference, and I have both the 5 and 5s side by side. There is maybe slightly less stutter, but things like opening spotlight still show a visible frame drop the first time. Nothing huge, but iOS 7 still has some creaky hinges that need optimization. Maybe 7.1 will be like snow leopard - new API's (Siri, Touch ID, etc.) and a ton of optimization.
Touch ID though is really nice, I used my passcode just now and it took forever in comparison. No home, swipe and 4 touches now just press home.
Also burst mode on the camera is awesome, the camera is just all around better than the 5.
As a test I just launched Asphalt 8 - iPhone 5 actually won with loading the app (Getting past the default screen, but that may have been because it was still in memory though.) 5s won in actual loading time, but only by about less than half a second.
I think we may see an actual difference once we start getting some heavier iOS apps which may happen when the iPad gets a 64 bit chip. Normal everyday tasks are only going to be milliseconds faster because they are limited by network/flash memory latency.