I have looked at this and read of the experiences of hobbyists here since 2002. I believe there would be good reasons to run an air stone bubbler rather than a powerhead.
1. A bubbler moves the water just enough, plus it has the advantage of efficient aeration delivering oxygenated water to the coral and fish and keeping pH from dropping. I might even buy several of these $14 battery powered, automatic switching air pumps that can run up to 48 hours on 2 "D" batteries:
http://www.thatpetplace.com/silent-air-b11-aquarium-air-pump-battery-operated2. My next choice would be to use my DC->AC inverter, but there are problems when running some powerheads on the Square Wave output from an inverter. Some won't even work on that output. I would either have to find the right powerhead or get an inverter that produces normal Sine Wave output.
3. I don't have much money for things like this so my last choice would be to get a portable generator like this one for $469:
http://www.homedepot.com/p/Champion-Power-Equipment-3-500-4-000-Watt-Remote-Electric-Start-Gasoline-Powered-Portable-Generator-46565/203589538?N=5yc1vZbx9nZ1z0z74fHope this helps,
Aloha
Edited by Mark Peterson - April 25 2014 at 7:31am