The F stop (ratio of objective diameter to focal length) is a static ratio, not affected by format (which is the optical target where the inverted image is cast). A 200mm F4 is a 200mm F4 regardless of whether it is put on a POS sensor, 4/3, APSc, FF, MF, or view camera. It casts the same light circle, hence the Contax-Zeiss view in the late 90s (great idea but derailed by the digital sensor train hitting it). F stop ratio is an inverted measure of "lens speed" which is still the classic term used in many optical engineering shops that look at exposure times.
The light circle is diffused the wider it is cast, and the angle of it hitting sensors or film is made more acute at the extremes. The smaller sensor "crops" but gets a higher quality light source due to less surface diffraction. Most sensors are designed with this in mind.
There is an effect on the extremes of larger sensors, but it is more to the negative than the positive. The FF argument "Larger is better" or a 24mpFF is better than a 24mp APSc, is the most ridiculous argument I have seen on this site (not this thread or the respondents). Anyone that takes that position is demonstrating their total lack of knowledge and ignorance... Simple. At 36x24mm sensor one needs 51mp to match the IQ of a 24mp APSc. Whew...