There is a third option....DC. I have a 12V camp and for a while I was buying 2000/4000W broken inverters to run the fridge etc. These were bundled in sales with smaller inverters. Usual problem was blown FET in H bridge. The smaller ones I just pulled out the H bridge FETs and ran pure 140V DC out to the outlet. Chargers, electronic CFL lamps, CD/DVD players etc work just fine on DC. Anything with a switching power supply. A little more efficient and less noise.
Built a camper in a regular sized passenger van (but without most of the seats) back before everyone and their brother were producing these. Ran across a small refridgerator which ran on either 12 volt DC or 120 AC. Had a battery charger under it and two extra 12 volts batteries which hooked to the alternator anytime the engine was running. Was young and stupid and hooked the two batteries in parallel. Next time it'll be two huge 6 volt batteries in series.
The battery charger failed one day and took out the transistors in the fridge.
In troubleshooting it, we discovered that the fridge ran on 40 volts AC. There was a transformer which stepped down the 120 volts to 40 volts, or stepped up the inverted 12 volts to 40 volts.
Drove it with the fridge cold for about 6 or 7 years, then sold it.
Tom