Another option is find and cpio, as follows:

find /source/directory -print | cpio -pdmv /destination/directory
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You can use arguments to find to select the files and directories you want to copy - by default it will copy the whole directory tree. By default cpio will not overwrite files with newer or the same modification time, so effectively it will only copy the new data. I often use '.' (current directory) as the directory in the find command.