[doldi]

The other option is kodi is not saving the changed settings. Perhaps something in .kodi is corrupt?
As a test can you rename .kodi (e.g. to .kodi_back) and reboot?
If you now change the audio device and reboot does it stick?
After confirming this you can delete the new .kodi directory and rename .kodi_back to .kodi. 

1) changing the audio device after rename Kodi and reboot = alsa_hifiberry does it stick.
2) after delete the new kodi dir. and rename kodi.back to kodi = after new start HDMI stands always in output device.

edit->sd card :.kodi is corrupt,
take the card from my pi2 and load the config.txt from pi3 on it (same addons ect) 

the fastest action to solve this problem.

Thanks, it works now and sorry for my flashy - helplessness. You understand me ;-)

best regards
Harald