From my experience, a compression fridge is way more efficient than a thermal fridge, i.e. a 3 way.
Well, that is correct if you are talking about electrical efficiency. Over a typical 24 hour period, a Compressor Fridge uses approximately 1/7th the power of a 3-Way Fridge
The idea of taking 12V and using an inverter to get 230V is SO inefficient. Transformers are passive, inverters take power even if no load, but if intelligent switch off and don't come on again.
However, THAT is such an incorrect statement
I have no qualms about runing my fridge (plus security system) 24/7 even if not driving with the back-up of an 80W
solar panel 8 months of the year. You need a compression fridge/fridge-freezer designed for 12 V plus
solar panels.
I love the way people like to make these absolute statements

You don't NEED a 12V compressor Fridge any more than you need a 240V fridge or you need a 3-Way absorption fridge. All will work in a motorhome and what is "needed" depends on the individual.
Remember, there is more than one type of efficiency ... two key ones to consider is ENERGY efficency and also COST efficiency, and both are important for most people.
In my testing over the last 10 years or so, I have found a 240V AC Fridge draws slightly less power than a 12V DC Fridge. The use of an
Inverter tips the balance over to the 12V DC fridge due to the inverters power overhead, but if you have a decent
inverter, it is a very close thing.
So ENERGY efficiency wise, it is pretty even.
But COST efficiency, the difference is nowhere near close. If it was neccessary to buy an
Inverter to support the AC Fridge, then of couse that cost efficiency is reduced (but still there), but if you already have an
Inverter in place for other purposes, then that is not a cost that needs to be added again, and the 240V AC Compressor Fridge wins hands down when compared like-for like for fridge size and features.