So, the general rule is that if you have the option when the power source is a 12 volt DC battery, power your device with 12 volts DC rather than using an inverter to first convert that 12V DC to 120V AC. You'll use less energy over all because of the losses inherent in converting one type of electricity to another.
The second rule applies if you don't have an option and must use an inverter because your device will only run on AC: size the inverter properly (not underpowered or wastefully overpowered) and spend a bit more money to get a high quality pure-sine-wave inverter that may be necessary for sensitive electronic or other devices.
