During a wifi test in my lab, I noticed that my iPhone 6+ showed awful performance. Both latency and speed sucked. I saw same problem on an iPad, but another iPhone and an Android phone had normal performance, indicating that the culprit could not be the access point.
The solution was to reset the network settings. There is a specific function for this in IOS, that can be found here:
Enter Settings -> General -> Reset -> Reset Network Settings
On both the iPhone and the iPad, the latency went from 300-700ms to 15 ms, and the speed was more than doubled. Awesome!
Note: You must re-enter WPA keys for all networks, since this information is lost as a consequence of performing the reset.
Learn how to change the settings by watching this video
DISCLAIMER: Obviously I cannot guarantee that this fix solved your particular problem with your i-device, but to me the effect was close to miraculous!