After tried CyanogenMod 10.2 (one of first nightlies, which was based on Android 4.3) I thought that something with WiFi sleep policy was wrong because as soon as I was turning off the screen the audio streaming services (like Spotify or Google Music All Access) started to stutter. I returned back to CM 10.1.2 stable but the same thing happened.
Initially I’ve contacted Spotify’s support, tried to return to a previous app version and because of any successfully result, I realized that something had to be wrong with my router during the sending of packets to my Nexus 4 in sleep mode (while screen on all was ok).
I’ve found these 2 router’s parameters which were the cause of the stuttering problem while screen of my device was off: Beacon Interval and DTIM
Beacon is a regular signal sent from router to report its activity state to stations and DTIM is the amount of time after which clients in power save mode are informed that their new data is available for transmission.
The solution is to decrease this 2 values until the streaming stops to stutter, for my network optimal values are those showed in the image.
Probably it’s not the general cause of all stuttering problems but give it a try.