My understating is that Nick is correct - for extended objects f-ratio determines the speed, not aperture.
If we take 10" f/5 and 4" f/5, the 4" will collect only 16% of the photons that 10" does. However, while keeping aperture the same, 500mm focal length will put 6.25 as many photons as 1250mm focal length (keeping aperture the same).
So if we combine both factors, aperture and the focal length: 0.16 x 6.25 = 1 On no! How can this be? 10" f/5 will be as fast for extended objects as 4" f/5? Actually, 4" f/5 will be somehow faster due to the lack of central obstruction and loss of light at the mirrors with the 10"
But for point sources, 10" will easily detect many many more stars than 4" and will most likely allow for a sharper image with tighter stars
