I've used both types of fridges. The fridge in my first unit ran on propane
only, cooled reasonably well but not as quickly as the compressor models. I'm currently using a Dometic compressor model (can't remember the model #) with a separate fridge and freezer compartment.
I have 200 watts of solar and a 140 amp/hour deep cycle battery. I can boondock for months at a time without needing to charge my battery from anything other than solar. We use LEDs, furnace
, fridge, stereo, water pump and CO and gas detectors as much as we want. Battery has never dropped to lower than 75% full charge. By 10:00am the battery shows a full charge and stays fully charged all day.
Without solar, the same battery would last about 2 days before getting to 50% charge at which point I would switch to another battery.
If your solar is working properly and you have a good battery you should be able to boondock indefinitely as long as you have a reasonable amount of sunshine. If I winter camp I do take my generator
and actually used it once.
If your battery dies after one night, it is either defective or you have excessive drain.