It seems like the answer to my question is (almost):
rsync -a -c --existing /source/ /destination/
This will copy files that are different from each other, and as I understand it, quietly synchronize timestamps of equal files.
As usual, try using the key -n(or --dry-run).
ADDED:
, . , script, , :
#!/bin/bash
SRC="$(dirname $1)/$(basename $1)/"
DST="$(dirname $2)/$(basename $2)/"
if ! [[ -d "$SRC" ]] || ! [[ -d "$DST" ]]; then
echo "Usage:"
echo " $(basename $0) src/dir dst/dir"
exit 1
fi
diff -rqs "$SRC" "$DST" | grep -Po "(?<=^Files $SRC).*(?= and $DST.* are identical$)" | rsync -tv --files-from=- "$SRC" "$DST"