I find this baffling; it's so far removed from my experience on my own iPhone 5 and to be honest it always has been, even on 7.0. I've been through every version of the OS since 2.0 and never found the speed an issue in IOS 7, particularly since 7.1, although I don't see the odd millisecond of animation as an issue anyway - the underlying system speed was always good.
As for crashes, it's rock solid and has been since the first update or two, and that's the impression I get from other iPhone users in my friends and family too.
I strongly suspect that those still clinging on the idea that there is something "wrong" with IOS 7 actually have something wrong with their devices. These isolated hardware-related issues are by no means exclusive to ios 7 and have plagued a minority of handsets on every OS.
Maybe if it were just one device. In my and my partner's family, there are 8 iPhones and 4 iPads, including 4S, 5, 5S, iPad 1, 2, and two Airs. They all have the animation delays. This is something built in to the system and something people have tried to address using various jailbreaks.
I agree that the underlying speed of the OS has generally been good, and
it still is with iOS 7. That is not the issue however.
The issue is that the animations, while much quicker than 7.0, disable the input of the touch screen entirely until the animation releases and control is active again. The biggest problem is that there is a delay where things look settled and ready to go, but theres another beat, if you will, before it starts responding. This can apply to the physical input buttons too (for instance, if you're exiting an app, then double tap to bring up the task switcher, it often will only catch one of those double taps... of if you lock and press the home button before the animation is done, it won't respond).
The reason it is so bothersome isn't simply because it's slow. The reason is you press a button or tap a virtual button when it looks ready and it ignores it, leaving you waiting to see if it will acknowledge it.
Worse yet is typing. I very often unlock the phone into an iMessage, the animation plays, it settles and the keyboard pops up... I start typing, and it doesn't start acknowledging input until I'm 1-6 letters in already; it makes a mess because autocorrect usually picks some other word based on what it received, you have to backspace and start over. If you see the keyboard, and it's settled in place, it should respond. There's simply no excuse for such a delay, especially considering how much better it used to be. I remember seeing a chart that showed how iPhone touchscreens are 10-20ms more responsive than the leading Android devices... yet a full second gap doesn't seem to matter.
I completely understand that this will only affect people who tend to use their phones very quickly, usually from muscle memory and habits learned on previous iOS versions. Plenty of people wouldn't be affected, although I personally know several who made the complaint without having been the one to bring it up.
If you'd like, I can try to take a video showing an iPhone 4S or 5 on iOS 6 compared with a 5S or iPad Air to show you the delays. The 5 on iOS 6 is by far the snappiest device we have.
PS Sorry this is long... I'm just trying to provide a detailed account for you.