Audio quality if HDMI question

The question is… Theorically, all players must offer the same audio quality if the audio output selected is HDMI, because all of the will send the same bits throught the digital audio, for the same music file…but, really that is true?

Could I expect better quality with Volumio than Kodi, by example, if the selected audio output is raspberry HDMI audio out, and not any DAC?