Lets say we have two image sensors, each one with 1MPixel resolution but differing in size. The first sensor has the size 1/3", the other one 1". Each sensor is equipped with a suitable lens (for the image sensor format, so no vignetting or cropping takes place). Both lenses have the same characteristics: F-stop f/2.0 and Ultrawide view angle circa 100°. Both sensors are running at 100fps, so that the image shown by the 1/3"-sensor is rather dark at normal illumination in a house.
Now how much does the image shown by the 1"-sensor differ (at the same illumination) in terms of brightness? I'd guess that the 1"-image would be much brighter because of the greater entrance pupil, is that correct, and if yes, how can I calculate which f-stop the bigger lens (which sits on the 1"-sensor) need to have to resemble the image brightness of the small sensor?