Hi Steve,
The inverter standby difference between uing a 300w as against a 600w is so small, ie, a few mA, so as long as you switch the inverter off when not required differences are not worth mentioning.
There should be no difference pulling 300w out of a 300w inverter, than pulling 300w out of a 600w inverter.
Your 12 volt amp requirement will be the same.
However, now your newer 600w inverter is only 50% loaded, you will expectedly draw more from it's rating of 600w.
The more you draw out the inverter at mains side, the more you have to put in at battery side.
If you have your 2 x 96 amp Hour (Ah) 12 volt amp hour batteries connected in parallel the in theory you have a capacity of 192 amp hour.
Ie: in a perfect world, you could have 1 amp delivered from your parallel batteries for 192 hours.
However you could not have 10 amps for 19,2 hours, and you really can't have 100 amps for 1,92 hours.
As said above, it is a discharge scale.
This discharge scale depends on the quality of your batteries, and their well being, ie, how many times they have been killed by a total discharge, and how old they are, by old, we mean how much lead has been shaken off the supporting plates within the cells. This lead which is shaken off the cells accumulates in the bottom of the cells, and may well eventually short out the plates which make the cells to a degree.
Good fresh batteries may give you 10 amps for 10 hours, where tired batteries may only give you 10 amps for 5 hours.
I used to give a good days work, now I am older now I find 5 hours is enough
Batteries of the sorts used here, like either long light discharges, down to a recoverable level, or mega 200 amps for a few seconds while cranking the engine over to start.
What they don't appreciate is total discharge.
This brings back to the "perfect world" ie, drawing 1 amp for 192 hours, it is just not available, you may get 1 amp for 60% of the capacity of the battery, before you start wondering into the realms of damaging the battery.
They can be recovered to a degree, but they can never be as good as they were before they were totally discharged.
It should be noted, that inverters now have voltage detection, and are preset to disconnect the inverter when the battery voltage drops to 11.0 volts, as a safe guard against this damage of total wipeout.
Better quality inverters have a user setting where this 11.0 volt setting can be adjusted, to take in account of speciality batteries, where lower than 11.0 volts, perhaps 10.0 volts, can be reached before inverter shutdown.
Have you considered a solar panel on the roof of the 'van ?
A 100w solar panel, via an intelligent charge relay is the way forward for you in France on an extended holiday.
I guess in France, June summer day, you will get 10 hours of sunshine at 100w at 13 volts to charge
Thats a good 7 amps an hour. Free except for capital outlay.
Gra.