Copying a file only when it is newer than the destination
Using the update option (-u) with cp should do it for you.
http://beginnerlinuxtutorial.com/help-tutorial/basic-linux-commands/cp-linux-copy-command/
rsync --progress -r -u /from/one/* /to/another/directory
You're not saying what shell you're using, so I'm going to assume ksh:
if [[ file1 -nt file2 ]]; then cp file1 file2; fi