SM74611: Isolating batteries with low loss diode

I have 2 12 vdc batteries of similar but unequal type. I want to isolate one from the other during discharge, none should charge or drain the other. Voltage drop must be small - there is a voltage cut-off circuit following which I can not alter. Operational time drops with lower voltage. Current is about 5 amp, peak may be 10. Load is music amplifier with built-in battery (1) and connector for external battery (2). Charger offers 15 vdc, 2A for the internal battery. I will charge while the batteries are disconnected from each other. Which component is more suitable SM74611 or LM74700? Circuit substitute: Battery 1 -> diode -> load & Battery 2 -> diode -> load. There is only 1 load.