A little device to control current flows
I like that problem !

Maybe you could try something along these lines (just from the top of my head, more to get a discussion started):







simulate this circuit &ndash; Schematic created using CircuitLab

note that left MOSFET is N-channel, right mosfet is P-channel but you need to check stability, I'm afraid even with the R9 resistor you could get all manners of oscillations from the mosfets capacitances.

The idea is that if current on the left is larger than current on the right, -input will be over +input so the op amp will move its output high , making the n-mosfet more conductive and the left one less conductive (and vice versa).

You need an op-amp with low enough offset voltage for the precision you want. It should also be able to work with low supply votage and Rail to Rail input.

However I'm not sure you can get a suitable p-mosfet for the kind of current you want (you can parallel them though). Also watch out for SOA since the mosfets will be in their linear region, they might get local hot spots on the chip (see that question and references therein)

I'd keep the resistors low enough to keep most of the battery voltage for the mosfet gates. Of course if the battery voltage is higher you've got more headroom and you can drop more voltage in the resistors.

EDIT

I think I misunderstood the question. I thought the purpose was to drain (equally) the batteries, not to share current provided to a useful load. My bad...

The suggested modification by KalleMP







simulate this circuit

wouldn't work since for a working load there wouldn't be any significant voltage left for MOSFET gate operation.