I have designed, developed and installed a number of solar controllers and panels. I never have faced any performance degradation. No adjustment is needed. Yes, a 24V controller cannot be connected to 12V.
Suppose the battery is disconnected. Will one controller try to 'charge' the other controller?
Nothing will happen. In most cases the charge controllers will not turn ON because they are designed to power up from battery. Even if this is not the case they will not charge each other. Power cannot flow back into the charge controller by design.
These are MPPT, designed to maintain highest ampere flow.
Correction please, MPPT charge controller are not designed to maintain highest current rather they are designed to maintain / extract maximum power from solar panel. Moreover controller have internal protections for overvoltage.
Now lets take an example, suppose that we have two charge controller one have float voltage at 27V and the other is 28V for a 24 volts system. (though in real life this much difference does not exist.). Assume that both controller are able to turn on without batteries.
Now let connect first controller to one set of panels. The output voltage will try to increase but then eventually settled at 27V. The controller will try to maintain the voltage. The same will happen for the other controller. The controller will try to maintain the voltage at 28V.
Now connect the two charge controller (Positive to positive and negative to negative). The voltage of first controller will increase from 27V. To maintain the voltage, the first controller will turn off its charging (No current flow). So, the voltage of combined controller will be 28V with almost 0A current (batteries disconnected). NO ISSUE OR HARM.