Here in N. CA we use both NAD84 and 27 depending on the maps.
People lost, tend to be in remote areas that are the last ones
updated by USGS and so we sometimes use the older map data if that is where the search is.

Some planes and copters we have dealt with cannot (or won't)
use UTM. And ground searchers in terrible conditions and dangerous
terrain shouldn't be using mapping methods that slow them down
(Lat/Lon). So we use both. And practice.

We also have use of a communications van which does the math for us.
If we are in a snow storm at night, it can be a bit hard or dangerous to stop
and figure out the other location data, so we simply call the com van with our utm coordinates and they can then speak to the planes using Lat/Lon. We also, of course, give redundant location information (land marks, section corners etc.) The com van will then help us plan a route around avalanche terrain and other obstacles and give us compass bearings etc. even if we can't see where we are going. They also track everyone on
computer and when a team returns they plug in the GPS and download
the route. At least once, we found the missing when the computer map
showed a small hole in our search pattern.

It is nice if your GPS units can quickly toggle back and forth from UTM
to Lat/Lon. We have a lot of older Etrex that take a bit of fiddling to
convert. Since we usually are in hasty teams of 3 or 4, one team member
can leave his GPS unit on Lat/Lon if we need to coordinate directly
with the planes and copters.

There is an advantage to just being able to read 6 numbers off as to your
location (UTM) when the radios are breaking up.