G.711μ (sometimes call mu-Law, uLaw, or PCMU ) and G.711A (sometimes called ALAW or PCMA) are 8kHz codecs which provide a bandwidth of roughly 300 Hz - 3400 Hz. This is the same codec as used on traditional analog telephone systems. μLaw is used in North America and Japan. ALaw is used everywhere else, and also when one leg of a call is in an ALaw region.

G.722 (which is not the same thing as the similarly-named G.722.1 or G.722.2 codecs) is a 16kHz codec which provide a bandwidth of approximately 50–7000 Hz. Therefore the intelligibility is much higher than G.711. In addition, it has better compression than the G.711 codecs, so it is able to send twice the number of audio samples in the same TCP/IP bandwidth.

SIP uses what's known as the "Offer Answer Model" to set up a call. During the call setup process, the calling phone- for our purposes here GCK is a softphone- presents a list of codecs it supports. This list doesn't necessarily have a "best", but SIP assumes that they are listed in order of preference. It's the job of the answering device to select the first compatible codec (taking into account its own preferences) to be used during the call. Its reply message "answering the call" contains the codec it selected, or a failure message if there was no compatibility, in which case the call does not complete, and the caller would probably hear a busy tone. This would only be a problem if the house system only offered (for example) G.729, which has happened. 

For dial-in, GCK selects the first codec in the list from the calling device, be that G.711 or G.722. For dial-out, GCK offers G.722, G.711u, G.711A, in that order. It will work for either Cobranet/Dante or IP Audio devices. The audio will sound like whatever the source audio sounds like. We do not degrade the audio, and it's impossible to add extra bandwidth to a G.711 source, even if it were trans-coded to G.722 (which can happen in the SIP world). That audio would retain the G.711 audio quality. In that case, there is actually a danger of making it worse by adding "artifacts" due to aliasing if the trans-coding is not done properly. In practice, however, we have not run into this.

You can test this audio quality yourself by going into the web portal on an attached phone (or softphone settings) and disabling / reordering the codecs to prefer or exclude G.722 or G.711. Saying the letters "S" or "F" in either codec is a simple way to demonstrate the audio quality of G.722 vs G.711.