Stu, the point I was making was all other things being equal, using an AC appliance running off of a DC Inverter is inefficient. It is more efficient to run a DC appliance off a DC source than an AC appliance off a DC inverter.
With that said, as we both know in the world of marine refrigeration nothing is equal. There are so many factors involved that affect efficiency, including the box design, insulation, compressor style and build, door seals, refrigerator location, and so on, that confound any attempt to simply answer the OP's question. Ralph was correct (again) that we need more information about the installation.