I'm looking for a multimeter that will be
used 24/7 on DC and mA readings. Are there,
in your opinion/experience, any difference in
long-term durability between the Fluke 87
(series 80) and the Fluke 81438 multimeters?

Tunes-

I'm not familiar with the 81438. The 87 may be similar to a 77 I used at work.

The 77 function switch has a vulnerability in that the knob and shaft that
activate it are attached to the front, and the switch and PCB are attached to
the back when opened to change the battery. The rotary part of the switch is
floating and moved out of position when the battery was changed. Damage to
contacts occurred when the meter was re-assembled.

You may prefer to call this "operator error", but I've never had any such
problem with my 8020A which has a separate battery compartment and push-button
switches. (Of course it is not auto-ranging!)

Given a choice, I prefer push buttons to a rotary switch, especially if
settings are to be frequently changed.

73, Fred, K4DII