The output wave most likely. It has to be a sine wave and CyberPower supposedly has simulated sine wave… I’m scratching my head at the moment…
This is pretty much EXACTLY what I found. Here's a forum post from a similar question...
"Being an Electrical Engineer, I know that most battery backup systems that you can buy in your local Wal-Mart or Target stores (APC comes to mind) that are strictly battery backup will provide essentially a square wave output when operating (versus a sine wave from the power company), and most pump equipment could potentially be damaged under such a power source - they're just not designed to operate on that type of power. So I would think that at most, you would just want to select one power head to put on battery backup and make sure you have enough established Live Rock in the system to support biological conversion during an outage."
This isn't my knowledge, just someone else who has a much better understanding lol.
They further went on to say:
"If you wanted to run the main pump off a backup system, I would think the ONLY way to do it would be to do it right, and buy a "True" Online Double-Conversion UPS. This device takes the input from the power company, converts it to DC, then back to AC to the equipment it supplies power to. The batteries are charged on the DC side. This type of unit provides a nice clean sine wave (it also cleans up the utility power signal so you will extend the life of your equipment) but it also costs quite a bit - usually $300 to $500. You will usually get longer running time also, since these are designed to keep a larger piece of equipment running, such as a computer server long enough to keep the system running during a short-term outage, and with enough time to perform a proper system shut-down once the batteries start to run out."
Hope any of that helps