Well, actually, the total light (number of photons) captured by a full frame sensor with the same aperture is 1,6² times more than the total light captured on the final image of a Canon APS-C sensor. You have to (basically) multiply the exposure with the area of the sensor to get the total light. That is the ground reason why the same generation of sensors with the same number of pixels on APS-C have worse high ISO performance (at image and pixel level) than the FF sensors.There are less photons to form the image both for each pixel and the total image on APS-C in this case.
Thus, the total amount of light hitting the FF sensor from an f4.0 lens is the same as the total light of an f2.5 (4/1.6) lens on Canon APS-C, as the aperture is calculated linearly against a single image dimension,( not f1.56, as previously claimed).
Of course, if you crop the FF image to APS-C in post, you get a more or less identical image with he same lens, but that is not the point here.