I notice quite a lot of latency with VoiceOver even when nothing is running and I'm using internal speaker or headset. 1: I can briefly touch an item on the home screen and move my hand quite a distance away before VoiceOver announces it.
2: Dragging around the screen often has delays.
3: Sometimes nothing happens when I touch the screen. It seems confused. I have to stop touching the screen for a while for it to work again.
I do not remember such delays in iOS 7.