DIfferent Battery Sizes ?

Yep, correct Mike.

And if one or more cells fail in one battery, it would cause the other battery to drain down (flatten) as well.

I prefer to have separate controllers for remote batteries.

My auxiliary battery is isolated from the starting battery by the Piranha controller.
My portable battery system is connected to the auxiliary battery, but through a separate in-car charge controller so it can be charged along with the auxiliary battery via the alternator, but remain isolated from the other batteries.

There are 6 cells in a 12v 'wetcell' battery

Question:
How many 'cells' are there in a 12v AGM battery ?

Mainey . . .

Same 6 x 2.2 volt cells

I use an in-car charging kit rated at 30 amps, purchased from Blue Apple (Home of 12 Volt).

This heavy duty charging kit incorporates an isolator in its makeup.

I don't understand why you believe you need to parallel both batteries together to run the fridge. Apart from changing from one battery to the other as one drains down, you would get the same elapsed running time.

In my setup, I use the auxiliary battery (80Ah) whilst travelling, then swap over to the 75Ah "Thumper" as I generally take the fridge out of the vehicle. Between the two I have sufficient capacity for 4-5 days minimum and supplement the Thumper's available capacity by "charging while using" via a solar panel.

The 30 amp in-car charging unit will restore the Thumper to a full charge in 2-3 hours or so of driving, depending on it's state of charge. In the meantime the auxiliary battery should be at, or near full charge, should I require it.

""I don't understand why you believe you need to parallel both batteries together to run the fridge. Apart from changing from one battery to the other as one drains down, you would get the same elapsed running time""

Sand Man-> An excellent reason for running a fridge from 'both' batteries is you only discharge 'both' batteries very lightly, and then recharging is very fast and far more efficient.
I'm sure you will also find the 'elapsed time' will be actually increased, due to the much higher battery capacity, because you will find the (quality) AGM battery will partly 'regenerate' itself during the fridge off cycle due to it's chemical make-up, this can be verified by my own AGM battery system still being 12.7v first thing in the morning after running a fridge and lights during the night.

By using only (1) battery it will cause this battery to be discharged much deeper, and yes most probably to the point of the "low voltage disconnect device" disconnecting the fridge from the battery, and when this happens while your away from the vehicle and therefore don't notice, then you will definitely have warm beer and an upset cook too.
If there is no 'low voltage disconnect device' then the single battery will be fully discharged beyond the point of being useful, if fridge is not changed over to the other battery at the correct time and the original battery recharged again.
If charged by solar it would not be a problem :-)

Mainey . . .