Here's a trick that almost does this, but this trick only works when you are copying to folders on the same server. Below is the relevant content from the included link.
[jonesy@cranford testing]$ ls
bar foo
[jonesy@cranford testing]$ ls foo
1 2 3
[jonesy@cranford testing]$ ls bar
1 2 3 4 5 6
[jonesy@cranford testing]$ yes n | cp -i bar/* foo 2>/dev/null
[jonesy@cranford testing]$ ls foo
1 2 3 4 5 6
[jonesy@cranford testing]$ ls bar
1 2 3 4 5 6
"I’m piping a constant “no” to the “cp -i” command, which asks you if you want to overwrite (or not) any files that already exist in the target directory. You don’t have to send STDERR to /dev/null — there’s just some messy output if you don’t. The end result is that the copy command will only copy files into the destination directory if they don’t already exist. It’ll skip files that exist in both directories (Well, technically the copy command won’t, but the operation will when you do it this way)."
"Of course, I could just forcibly overwrite the directory contents, but I don’t know if the files that exist in both directories are identical. Or I could move one sideways and the other into place, but the same issue exists."