A diode-type isolator doesn't change that.
Okay, yea it prevents one battery from pulling down the other, but it doesn't change how the voltage regulator behaves. The voltage regulator only sees that the voltage is either below the set voltage or not. As long as the voltage is below the set point, it keeps the alternator turned on and each battery sucks up however can overcome its internal resistance. Doesn't matter if they are the same type, age, capacity, etc.
As for one battery sucking down the other - not so much of that going on there. As long as both batteries are tied, and the secondary battery is lower, then the bus voltage will be drawn down, causing the voltage regulator to keep the alternator on. So the secondary battery is drawing from the bus. The bus has two sources of supply - the alternator and the primary battery. The alternator supply has a lower resistance than the primary battery, so almost all, if not all, of what the secondary is drawing is going to come from the alternator.
That will go on until both batteries have a surface charge equal to the voltage regulator set point and the voltage regulator turns off the alternator. After that, the secondary will drop down from surface charge faster. In that situation, the secondary could draw from the primary, but the voltage regulator is going to kick the alternator back on anyway, so it's not like the primary gets drawn down by any noticeable amount.
Batteries only need to be identical if they are tied into a permanent bank. If they are only tied during charging, then the only thing that matters is that they both require approximately the same charge voltage.
EDIT: Well, what I just said is true with a constant voltage charging system, such as a voltage-regulated alternator, or a two-stage charger (bulk/float). It's not true if using a 3-stage charger that does absorb. With a 3-stage, you don't want to mix batteries during charging.