ECRoyce said:
surapon,
something you mentioned in your initial inquiry looks like it went unmentioned so far (unless I missed someone's comment). mAh is the capacity. it is literally milli-Amp hours, mA x h = mAh. theretically, 2000mAh would run a 0.1amp draw for 20 continuous hours, or a 20milli-amp draw for 100 hours. It has nothing to do with the amount of power hitting your device, or the 'size of the pipe' (which would be voltage).
So your concern that your flash would be damaged by the higher mAh is not a valid one. Think of it as a larger gas tank. I WOULD however, be concerned with construction (which battery could split/leak components inside your flash damaging it chemically) and the reliability of the cheapo brand, and like others have said, self-discharge rate (loss of power while not in use).
Eneloops like everyone says, are good due to their low self-discharge properties. Another Low Self Discharge battery I have tried with decent success so far is Tenergy brand Centura model. They are a little cheaper to compete with Sanyo's Eneloop line and to me seem to be 'as good' comparing to the ones that I have, but of course Sanyo has the longer track record with their design.
Sorry, but your logic is flawed. Yes, the capacity measured in milliampere per hour is related to the time at which the battery can supply the rated voltage of 1.2 volts. But... The actual voltage at the time of a peak current drain naturally falls. ??? I remember that alkaline batteries have actually 1.7 volts when new, but drops to 1.1 volts, at the moment of recycling flash. :

On the other hand, the Ni-MH batteries has 1.45 volts, but when the flash recycling, drops to 1.2 volts.

Thus, at the time of peak current drain, NI-MH batteries provide higher voltage than Alkaline batteries. 8) Now, imagine a hypothetical NI-MH battery that has truly 8000 milliamps per hour. :

With such capacity, the voltage drop would be smaller. Perhaps would drop to 1.4 volts, providing flash recycling time faster than ever (4 x 1.4 volts = 5.6 volts).

It turns out that the flash supports 6 volts when in standby, but provides for a natural fall at the moment of recycling. If does not happen this fall, it would cause overheating of the flash circuit which was not designed for such high voltage.

Another practical example: If the flash work with nominal voltage of 6 volts, we can use lead acid batteries 6 volt and 1800 milliamps (external) without causing damage to the flash. But if we are to make thousands of shots without changing the battery, then use a lead acid battery 6 volts and 8000 milliamps... ??? And the flash recycle time will have a super-duper fast because the voltage drop will be null. :

The result is that the flash circuit will be toasted because of the excess voltage not dropped at the time of recycling. :-[ Bottom line: If a device is designed to use 2000 milliamp battery safely, you should not use battery with much higher amperage than that. :-\ Of course, to obtain a secure long term use without replacing batteries is the accessory "
Canon CP-E4" that transforms the correct voltage, using 8 batteries simultaneously.