http://en.wikipedia.org/wiki/Solar_cell_efficiency#Maximum_power_point
If you draw too much current from solar cells their overall efficiency falls. This is evidently affecting all three configurations to different extents. If you test with a set of resistors in the 1 - 20 ohm range you'll get different results. Given the power dissipation it may be easiest to do this with automotive lightbulbs of different wattage ratings (higher wattage rating for same rated voltage = smaller resistance). Ideally you'd want an adjustable 20W dummy load.
First, please don't try "supply fight" shenanigans in practice if you don't know what to expect.
Assuming both sources are exactly 10V, the current capacity wouldn't matter. Just use Kirchoff's circuit law as usual: 10V on one source, -10V on the other, so 0V on the resistive load. V=RI=0, I=0, no current.
Current capacity would matter if:
1) There was some voltage difference between the sources;
2) This voltage difference causes enough current to flow through the circuit so as to overload the current capacity of one or both sources.
In practice, there are probably no two sources that produce the exact same voltage, so condition 1 will always be true. However, condition 2 rarely will be satisfied: you need a large I, so you need a large V/R. If both sources are rated as 10V, they probably shouldn't differ much, so V will be small. And R will be at least the sum of the output impedances of the voltage sources.
If you actually want to explore how the current limitations would affect the outcome, you should consider what happens when 1 and 2 are true. I'd suggest assuming that one voltage source is +10V/10A and the other is, say, -9V/100A, and R is sufficiently tiny (say 0.05 ohms).
Best Answer
It is a basic rule. The physical basis for it is as follows. Current is just moving charges. Charges cannot accumulate. That is, objects generally cannot acquire a net charge. That is both a physical rule (rule of the universe) and also a rule for circuit analysis. So every time charges move into one side of a conductor, an equal number of charges has to move out on the other side.
So if I2 is dumping charge into the conductor at 10A, and I1 is clearing charge from the same conductor at 5A, that would imply that charge is accumulating in the conductor. Since that is impossible, it is impossible for two current sources to be in series unless they have the same current.
I hope you find this to be a satisfactory answer. I have tried to be accurate but intuitive. There are lots of analogies that could apply also (cars on a freeway, or skiers getting on a ski-lift or something). Let me know if you want me to offer something of that nature.