Choosing leds for batteries power

The datasheet will have this information. Some LEDs that can only handle 20mA continuous are spec'd for very brief pulses of a much higher current. You would have to specify the PWM frequency to be able to look up the answer to this question in a datasheet.

For one particular product, the CREE CLV1A RGB LED, you may drive red at 50 mA continuous or with a 200 mA pulse (pulse width ≤0.1 msec, duty ≤1/10), and blue and green at half that current. It's all in the datasheet. You can also see that there is a diminishing return as the relative luminuous intensity vs. forward current is not linear at high currents.

I think you should not worry about the brightness loss from driving your LEDs at a 50% duty cycle at the maximum continuously rated current. IIRC the eye has a non-linear response to brightness and they will appear somewhat brighter than half as bright, and you won't destroy your LEDs if you screw up the PWM.

It is highly likely that your red LEDs are of lower luminous efficiency than your white LEDs.

Also, driving an LED incorrectly can destroy it or reduce it's output from then on. Such damage can occur almost instantaneously. Red LEDs have lower operating voltages than White LEDs so are more likely to be damaged by the application of a constant voltage that is too high and not current limited.

The efficiency of LEDs varies widely. It can be expressed in lumens/Watt = l/W.

The best white and the best red LEDs have similar enough l/W ratings that both should appear about equally bright when driven with the same power input. White LEDs typically have operating voltages = Vf in the 3.0 - 3.6V range and red LEDs have Vf = 2.0 to 2.5 Volts. So a red LED would need about 50% more current to achieve the same power as a white LED as Power = V x I.

You state the LED output range as 500 - 20,000 mCd. That's a 40:1 brightness range.

Note that candela are a measure both of energy out and area of illumination. Less area = more brightness for the same light energy.