According to the Specs
The official documentation doesn't actually contain a power spec. https://www.raspberrypi.org/documentation/hardware/camera/README.md
The FAQ's do offer some guidance: https://www.raspberrypi.org/help/faqs/#power
The Camera Module requires 250mA
This is measured as additional current from the 5V supply.
Calculating the Power
Ohm's Law says: Power = I * V (current times voltage) so P = 0.25 * 5 = 1.25Watts.
The above answer is likely the maximum power the camera uses when in operation, so an upper bound. This isn't a bad question especially if you're trying to build a solar powered pi. It's woefully difficult to find this basic information online!
According to one of the Raspberry Pi engineers and forum moderators Source: https://www.raspberrypi.org/forums/viewtopic.php?t=152864
the original Pi Camera board v1.3 camera takes about 200-250mA.
Assuming that's measured off the 5V USB input to the Pi, you could assume 5*.25 = 1.25W power usage maximum, and 5*.20 = 1W minimum in use.
The Pi camera 1.3 is based off the sensor by Omnivision the OV5647, BOTH for the regular and NOIR versions.
According to GoPhotonics, the sensor itself draws 96mA from a 3V input. https://www.gophotonics.com/products/cmos-image-sensors/omnivision-technologies/21-118-ov5647
However there's likely a voltage regulator in the camera circuit using more power (i.e. turning 3.3V on the Pi CSI connector to the 3V the sensor needs).
Note: the "NOIR" means a small filter which filters out IR from the sensor, has been removed. That is a mechanical change, and shouldn't affect the power draw. So we expect power usage to be the same between regular and NOIR versions.
How to get a better answer
As far as comparing to the 'knock-offs' - my recommendation would be to see whether your flavor of knockoff is using the OV5647, and then get a basic USB inline ammeter and report back to us! e.g. like this (click for full size):