My audio streaming app is working correctly with only WifiLock.
But some devices report that when they turn off the screen, connection is cut and audio streaming is
Use them both. The behavior I am sure varies from phone to phone. You may wish to search for the devices the reports are about + "wifi"or "wifi driver". Are you sure your audio streaming app is working correctly with only WifiLock ? This sounds very strange - the CPU will go to sleep and the service will stop - see Service, WakeLock. Something else is keeping the phone awake. So you need a wake lock
If you only use wake lock on the other hand the wifi will turn off maybe - I am not sure for you are using it - but better safe than sorry. If it does turn off waking the phone up won't wake it up - for this I am sure. Using the wifi lock has no impact on the battery - using the wifi radio has, and this you are doing anyway.
So both - and be sure your service acquires them - have a look at WakefulIntentService