If you have an HUSBZB-1 on your C-4, which does both Zigbee and Z-Wave (unless you have a second external Z-Wave stick, e.g., in non-North-American markets; the C-4 has no built-in radios, so if you have devices of both protocols, you have something for each), you can move that over to your new hub. Coupled with your hub backup, that should cover both your Zigbee and Z-Wave devices. (That being said, I had bad luck moving a Z-Stick between two hubs once, which should have been easy...not sure if that was bad luck on my part. They were different models, a C-5 to a C-3. I ended up just redoing all of those.)
In the absence of doing that, you can just restore the hub database. Resetting and re-pairing your Zigbee devices to the new hub with the database will cause the hub to recognize them and slide them back into the same "device" they were before. This means you won't have to redo any apps/rules (except Groups and Scenes; go into any group and click "Done," since resetting a Zigbee bulb/plug will also erase its internal knowledge of what Zigbee group IDs it belongs to). In my experience, this is pretty easy--I did that instead of moving the stick from my old hub when I got a C-5. Your level of patience may vary depending on exactly how many devices you have and how easy they are to reset. 
Good luck, no matter which way you choose!
