It's definitely a bit of a philosophical debate, and it'll probably vary from tank to tank, but powerheads would be near the top of my list, with heating/cooling second depending on the season and the home's ability to maintain a good temp without power.
Gas exchange is especially important when lights are out, because NOTHING in the tank is photosynthesizing. Everything is consuming oxygen and producing CO2, which means the gas concentrations in the tank are going to be off the charts in no time. Besides the direct impact (not enough oxygen) this will have secondary effects - pH will start to tumble, etc.
Waste products can take a few days to build up, especially if you're not feeding (who would during a power outage?) but gas exchange can cause problems in hours. I've never had an outage disaster with a reef tank, but I did lose power several times on my planted FW 60g (thank you, faulty GFI!) Even though I discovered these outages within a few hours, the CO2 concentration was already off the charts, pH was low, and fish were gasping at the surface. Temperature was only off a degree or two - nothing to worry about. Nutrient levels were spot-on - nothing to worry about. But a powerhead on a battery backup would have prevented the gas exchange problems and helped save the livestock.
Arguably the best solution is to just have a generator, and test your equipment on it so you know what will work and what won't work. Many cheaper generators and UPS's put out pretty clunky A/C and some pump motors won't run well or at all on them.
Though, a small portable generator won't automatically turn on if you lose power when no one's home, like a battery backup will. So maybe the best combination is both - the battery backup is a minimal life support system until the user can get a generator running or make other arrangements.
Again though, just my perspective, to each his own.
