With HDMI, you get to enjoy Lossless (or uncompressed) multi channel audio formats sent via PCM (digitally) that you can only get otherwise with analogue.

There simply is no comparison to the sound quality this provides over digital and coax because they are limited to bandwidth that HDMI is not. And even with 6/8 channel analogue, you do not get to take advantage of digital EQ’s or bass management.

With 5.1 HDMI, you still get awesome 5.1 uncompressed audio. The 5/1 or 7/1 argument is meaningless in this regards.