The Z at the end of the model number means it is RoHS compliant,.
It means it does not contain one of the 6 dangerous chemicals/metals that have been used the the manufacturing of electronics.
Or something along those lines.
So Z or no Z, should not make any difference.
I've only seen one post about the AD797 being "cranky" chips, so it's not something I'm worried about.
The AD797 seem to be the higher rated, per "The Xonar Essence STX Q/A Tweaking Impessions Thread".