That's a good solution. I was going to mention GNU cp. I'll do it here to keep mv and cp together in the suggestions.

I'd like to point out to the OP that both support the -u option for copying or moving only updated files. So one can keep the original copy of the newer file with one or move it with the other depending on changing needs, and it's still the same option to trigger the same semantics of only acting if the source file is newer than the destination.

GNU cp also can work recursively with the -r (or -R) option. With both (-u -r ) it can recursively copy directories and only overwrite an existing file if the source file is newer than the destination file or if the destination file doesn't already exist.