What is the most efficient and reliable method for transfering/copying a large number of files from one external hard drive to another?
If you would like to copy drive A to drive B exactly you can do this with Disk Utility.

We will be using Disk Utility's restore function. Some background on the different between Restoring vs copy and pasting:

The Restore function in Disk Utility makes use of a block copy
function that can speed up the copy process. It also makes an almost
exact copy of the source device. When we say &quot;almost exact,&quot; we don't
mean to imply that useful data may get left behind, because that's not
the case. What it means is that a block copy copies everything in a
data block from one device to the other. The results are almost an
exact copy of the original. A file copy, on the other hand, copies
data file by file, and while the file data remains the same, the
location of the file on the source and destination devices will likely
be very different.
Using a block copy is faster, but it does have some limits that affect
when it can be used, the most important being that copying block by
block requires that both the source and destination devices be first
unmounted from your Mac. This ensures that block data doesn't change
during the copy process. Don’t worry, though; you don’t have to do the
unmounting. Disk Utility’s Restore function takes care of that for
you. But it does mean that neither the source nor the destination can
be in use when you use the Restore capabilities.

Source: https://www.lifewire.com/use-disk-utility-to-clone-macs-drive-4042367

Instructions
for copying all files from Device A to Device B

WARNING: When you restore one volume to another, all the files on the destination volume are erased. Before you restore a volume, copy
any files on the destination volume that you want to save to a
different volume.

Choose View &gt; Show All Devices.
Select the volume in the sidebar you want to restore, then click the Restore button  or choose
Edit &gt; Restore.

This is the volume that is erased and becomes the exact copy. [Device B]

Click the Restore pop-up menu, then choose the volume you want to copy [Device A].
Click Restore, then click Done.


Source: https://support.apple.com/guide/disk-utility/restore-a-disk-dskutl14062/mac