Use rsync. It will synchronize the directories in one direction. So, if you want to update your old folder with everything from new, but keep what's in there, just use:
rsync -avh --dry-run /path/to/new/ /path/to/old/
This will, in a first instance, just output the list of files that would be transferred. In that case: Everything found in new will be copied to old, unless it's already there. Everything in old stays as it is.
If it looks fine to you, remove the --dry-run argument to transmit them for real.
The -avh flags just enable archive mode (which will preserve timestamps, etc.), verbosity and human-readable file-sizes. Nothing will be deleted from the destination unless you specify the --delete flag. Consult man rsync for more information.