If the fridge is say a 10Cu with the upper part being freezer. I can say that the larger inverter should start it up with little to no issues.
Is it a puresine ? or modified /MSW that you are looking to buy ?
The startup of the fridge can be around 10x the running load. It's the whole compressor startup that needs the extra power.
You certainly do seem to have enough oomph on the battery sizes.
A small answer to your original post about efficiency. Ture the larger ones will use the "juice" faster, but ,,, then you can safely run everything from one.
Efficiency wise, you'll want to run it at 70-80% full for the unit's size. Even on standby, it'll be using the juice quicker than the 1000w, just sitting there even with no load. The % of load could depend on the inverter itself. I have yet to run my 3000 watt MSW HF cheapo over 2000w , even then it tends to be pretty warm on the top.
Hope this helps
Bruce S