Mumble currently uses CELT and Skype currently uses Silk.

The two codecs have been merged/improved into Opus, which is one of the mandatory audio codecs for WebRTC.

But all three are moving to Opus, so very soon it's not going to be the codec itself that will differentiate audio quality between them.

I don't think it's about compression. I think Skype's invested most of their resource into, eg. noise and echo cancellation, reducing environment noise, working around glitchy / clicky sound capture devices, latency, ...