Jim Burns wrote:

Is the DME associated with an ILS a "low power" or special version that is
different from that installed in conjunction with VOR's?

Some of them are low-powered when frequency protection is an issue. Others,
like those for the west runways at LAX are intended to be used far out to the
east.

You would have to get in contact with someone in the FAA at Airway Facilities
(a service organization within ATO) to obtain the definitive answer to your
question.

Even where power is reduced, all required DME fixes must pass flight
inspection.

It might be a combination of lower power and your aircraft's DME antenna and/or
avionics.