If the aperture was a toll booth and we charged each photon a fare, then indeed, the 8x10" 210mm lens would pay a higher toll than the 4x5" lens, assuming it's area of coverage is much greater. So indeed, it's letting in a larger total quantity of light but not light of a greater intensity.

This extra light is due to lens design and coverage alone, it really has nothing to do with the f/stop.