There isn't much information or a datasheet for the IR camera in the wiimote, but it has been reversed engineered so that it can even be pulled out and used via i2c.
Some testing shows:
The sensor is at least 5 times more sensitive to 940nm than 850nm. This disparity increases slightly with the removal of the filter window. Relative sensitivity to visible is not known. (wiimoteproject wiki, archived)
To determine the relative sensitivity of the Wii Remote, two leds with similar characteristics were used: SFH4231 (940nm, 180mW TRP @ 1A) and SFH4230 (850nm, 200mW TRP @ 1A). Both devices provide an approximately Lambertian distribution of light, with a 1A maximum continuous current and 1.8V drop.
The LEDs were attached in series with a laboratory power supply, 5-digit ammeter, and 0.5-ohm resistor. The LEDs were positioned vertically approximately 30cm apart, facing a Wii Remote approximately 5m away. Measurements were taken with camera gain values between 0x10 to 0x40 and minimum blob size of 3. For each configuration, the minimum current at which each LED became visible was recoded. Gain values higher than 0x40 resulted in the 850nm LED being undetectable even at 1A.
Without filter window in place: The 940nm LED was detectable with approximately 12% the current required to detect the 850nm LED.
With filter window in place: The 940nm LED was detectable with approximately 15% the current required to detect the 850nm LED.