Hi,
Because of the Peukert effect, batteries wired in a balanced manner will allow more total amp-hours than using them individually.
It would be best to equalize both batteries individually to get them up to the greatest possible capacity.
Recharging from the generator should be done with the existing converter, if it is a modern three stage. Additional chargers can be "piggy backed" up to the limits of what the generator can power watt wise.
The output from the EU1000 is unregulated, and limited to only about 8 amps. That is a poor way to recharge a battery bank.
This is what is balanced and best for twin twelve volt batteries.
As it often doesn't cost a dime more to do this, I think it is worth the trouble.
If you wish to understand the "why" surf here:
correctly interconnecting multiple twelve volt batteriesOthers may say it doesn't matter--but unless there is a compelling reason to not optimize charging and discharging why not do it the best possible way?
Regards, Don
My ride is a 28 foot Class C, 256 watts solar, 556 amp-hours of Telcom jars, 3000 watt Magnum hybrid inverter, Sola Basic Autoformer, Microair Easy Start.