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Indeed, the operation should be line based, rather than word based, since file names can have spaces in them.

Compare:
echo "${array1[@]}" "${array2[@]}" | tr ' ' '\n' | sort | uniq -u

with:...

$DIFF in not an array but a scalar variable.
Try also
IFS=$'\n'
echo "${array1
}"$'\n'"${array2
}" | sort | uniq -u
Mac meDon't forget to reset IFS to your default value.