Z906 and Z623 are awesome for movies and game but not that awesome for music.
It is only good in music, not awesome.
Z906 is 5.1 system and Z623 is 2.1 system, if you put the 5.1 and 2.1 channel topic/differences aside, both have quite similar sound quality.
Z906 is the better solution for games and movies since it is 5.1 system but quite a lot more expensive.
For a 5.1 system, try to think were you should place the surround satellites before buying. If you can not find any suitable places, I would say get/keep the Z623 2.1 system.
Placing is the bigger issue for 5.1 systems.
Z906 is a nice upgrade to Z623 from gaming and movie point of view, if you can solve the speaker placement issue.
You will like the better surround sound in games and movies with Z906.
For music, nothing will really change.