The group member passwords are set from top to bottom, in order, as displayed on the password reset prompt.
This generally flows from most privileged to lease privileged, i.e. Enterprise Admins > Domain Admins > etc.
If a user is in multiple groups, the password will only be set once, at the highest privilege level.
Assuming that both groups passwords are being reset, this would operate like so:
If a user is in Backup Operators and Domain Admins, it will get the password set for Domain Admins.
If it was in Enterprise Admins and Domain Admins, it will get the password set for Enterprise Admins.
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