a 2400mah cell likely never hits overcharge.
so it avoids the abuse.
It is completely wrong to assume the higher nominal capacity cell (of the same size) will be more robust, it is exactly the opposite.
First the internal temperature load is given by the ability of the cell to dissipate heat vs the excessive power it gets. When the cell sizes are the same, so is the power delivered by the solar panel, as well as the ambient temperature from the sun, there can not be any difference at all.
The difference could be in the internal cell construction in how high temperature it may tolerate before starting to deteriorate. And there the most likely situation would be the more robust, higher temperature construction will most likely occupy more space, so for the same can size you may fit only lower capacity electrode roll.
Similar if you want to use larger excess of the negative electrode area, allow for faster and lower pressure water recovery reaction. That means you occupy more of the space by something that does not bring you any charge retention capacity, so less of the energy storage part will fit into the can, hence lower usable cell capacity. This is the main difference between "consumer" and "solar" cells - "consumer" are optimized for maximum usable capacity, assuming only minimal overcharge (just for the cell balancing, so some 10% or so), yielding capacities in 2500mAh and more.
On the other hand the "solar" cells are expected to be heavily overcharged, so the volume is nearly full with the "extra anode area", yielding just the 600mAh for an AA size.
And another way to allow for a short time overcharge robustness is to leave a void in the can. That space will become a gas storage buffer for a fast overcharge burst, allowing the gasses to be recuperated later. That means you have less space for the actual active cell assembly. It has an advantage of spreading the heat load over longer time, but it is not able to increase the average overcharge load as the previous. This is very common method for cheap solar cells - as side effect it saves the costly active assembly, it means just leave part of the can empty.
If the solar panel has in average higher power than the device consumes at night, each day will the state of charge be higher. Till it hits the overcharge. But that means, the cell will be handling overcharge for some time. Maybe not when first installed, but after few sunny days. The only thing the higher capacity brings is the longer time it will take to reach that level.
So e.g. with a 50mA average charging current at 12 hour day and 30mA average discharging current at 12hour long "night", that means each day the solar cell delivers 120mAh excess charge, so a 600mAh cell will reach full charge at the first two daya, from the days it will be overcharged by about 120mAh/day, assume about 20% cycle charge inefficiency.
A 2400mAh cell will get fully charged after 20 days, then again it will get 120mAh/day overcharge. The thing is, into a 2400mAh cell the cell maker may fit less of the negative electrode extra capacity (needed to recombine the O2/H2 generated during overcharging) compare to a same size "solar" 600mAh cell, so because the overcharging rate is the same, it needs highre pressure buildup to get sufficient recovery reaction rate. And the extra pressure means more stress mainly for the seal, so it will more likely fail sooner (assume the difference is only in the relative electrode sizing, not in the overall build quality).
The true "memory effect" is not anything permanent, nor real capacity loss. It is just some 100mV voltage droop when youstart to discharge the cell below the minimum limit you were operating the cell in the partial cycles before that. But after this deeper discharge, the "memory" gets totally "erased".
In a real world, the true "memory effect" you will never encounter with reasonably designed devices (to utilize even the alkaline cells more than half of their available capacity, the device has to be able to work below 1V/cell even when the rated voltage is 1.5V/cell; that is way enough to completely swallow even a heavy "memory effect" build up inside a NiCd cells).
What is observed in a real world is mainly the internal resistance increase due to cell wear, mainly caused by high cell loading (mainly ase for the common digital cameras or other similar devices). This is not recoverable, but it is not caused by the cycles being just partial, but by any high current loads (digital cameras,...; anything above about 300mA is high current for an HR6) and high temperatures (overcharging, devices kept inside parked cars) and/or other cell abuse (includes deep discharge with one electrode reversal, so with voltages below 0.6V on any cell, high internal pressures during high overcharge rate,...). Dont forget the separator (so the piece of material between the electrode foils, soaked with the electrolyte) is intentionally designed to close its pores (so break the electrical conduction) at high temperatures as a safety measure (preventing cell bursting when short circuited,...; the associated heat closes the pores, so breaks the circuit inside of the main cell structures). When the cell is exposed for high temperature, the pores start to slowly close down, so gradually increase the cell internal resistance. This is the most common EOL mode for NiMH cells I've ever seen, often misdiagnosed as a "memory effect"...