Batteries in parallel are always at the same voltage. Once capacity drops in battery 1, it's voltage drops, which shifts more of the load to the battery 2 with more capacity because it doesn't have as large a voltage drop. If there is any voltage difference between the batteries, current will flow from the high voltage battery to the low voltage battery. Under load, this will simply be an uneven outflow of current from the batteries, not transfer between them.
The ratio of how they drain may be variable and a little erratic, but you will have 600Ah of usable capacity. Once you get to the lower end of it, you may experience greater voltage drop and may not tolerate heavy loads as you would with a single 600Ah battery.