Audio delay that doesn't create lip-sync is expected behavior from any advanced receiver or pre-processor. This delay will become larger when advanced video processing is enabled. Essentially, the processor must "record" and "watch" the video for a few milliseconds to determine how to correctly process it, to process it, and then "play" it on the video output. This additional delay should be automatically added to the audio to compensate. Where the automatic compensation is not sufficient, the processor provides an option for further delaying the audio manually.
The problem with the Onkyos is that it seems there is a lip-sync issue where the audio is delayed more than the video, a problem that cannot be adjusted using the controls. Whether this is because of a firmware bug or because of excessive audio processing requirements, I don't think is known.
You can create audio delay problems by not routing audio and video through the same processor(s). For example, by running video directly to a display device or through a different path (e.g., a separate video processor). Some people with Onkyos clearly encountered this problem, which is arguably of their own making (not to minimize the apparently legitimate problems with the Onykos).
You can also experience an audio/video delay issue when playing games that require split-second hand-eye-ear coordination. Some video processors have processing modes specifically designed to sacrifice some processing quality for speed to minimize this issue. The Denons do not have such a mode. The correct solution in these cases is to disable video processing, as dem mentioned.
As far as I can perceive, the Denon 5308 has no lip-sync issues.