cpio

The -depth option to find ensures that directory names are output after the names of the files in them, not before. In combination with the --make-directories (or just -d) and --preserve-modification-times (or just -p) options to cpio, this results in cpio preserving the original modification time of both files and directories.

This works because cpio will create a directory automatically while writing the files inside it; only after it is done writing all the directory contents does it visit the directory itself to set its attributes, which includes resetting the modification time.

You are missing a couple other important options, though: the -print0 option to find and the --null (or just -0) option to cpio cause find and cpio to write and read the list of filenames terminated by a null character instead of a newline. Since most Linux filesystems allow names to contain nulls, this is important to properly archive such files and avoids doing something very bad with a file named like:

byebye<newline>/etc/passwd

So the full recommended command is:

$ find . -depth -print0 | cpio -pdm0v dest_dir