DME ident is
a) quieter
Not sure this is true in all cases. My local DME station audio is much louder.
VOR and ILS frequencies are paired with specific DME frequencies, so it naturally follows that if you have a VOR or ILS frequency selected, you will get the appropriate DME station (and audio).
Are you comparing the NG to other aircraft which may only pair the DME audio with the ILS audio if the Navigation Displays are in APProach Mode?
Does your NG allow you to tune both a VOR frequency and an ILS frequency at the same time on the same panel?