Think in terms of using a 4x5 reducing back on your 8x10 camera.
Whether or not you use the reducing back or the full 8x10 back, the intensity of light hitting the centre 4x5 of the film is exactly the same.
The difference comes from the fact that, for a given subject distance, the 210mm lens designed to cover 8x10 needs to be able to accept light and render detail from a much wider angle than the 210mm lens designed to cover just 4x5.
If you use the 210mm lens designed for 4x5 on the 8x10 camera, for a given subject distance the centre 4"x5" part of the image on the 8x10 film will be substantially the same as if you had used the 210mm lens designed for 8x10. Outside of that 4"x5" portion though, the "smaller format" lens will most likely vignette and/or lose resolution.