I have a 240mm El Nikkor and a 300mm Rodagon and used to have a 300mm El Nikkor. When I first got the 240mm, I did some comparisons with the 300's at 16x20 and 30x40 enlargements from 8x10 negatives.
The centers of the prints with any of the lenses were pretty much identical at both magnifications. I found the 240mm actually slightly sharper in the corners of a 16x20 print than the longer lenses, I assume because of less diffraction effects with the shorter focal length. In a 30x40 print the 300mm lenses were a little sharper in the corners due to more coverage with less extension, but especially with these larger prints, the longer lenses are more of a pain to use. The sharpness differences were very small and only really noticable with careful side by side comparisons. It's hard to remember, but I think the sharpness difference was larger at 16x20 than it was at 30x40. I didn't test at 20x24, but from the other two sizes, I wouldn't expect you to see any significant difference between the two focal lengths.
I could see no difference in the evenness of light with any lens with my enlarger--an 8x10 De Vere with a color head--but if your light source is only marginally large enough for 8x10 or it's located a long distance from your negative, the 300mm should give more even light (you don't need as big a light source because of the smaller angle of view).
I'm sure that there are some differences between different 240mm lenses. At some point, I tested a 240mm lens that Besler sold (actually the Rodenstok labeled verson of that lens, can't remember the name). At the center through slightly more than the coverage needed for 5x7 it was very similar to the performance for my El Nikkor. I would have been happy with the sharpness. However, at the edges of the print from an 8x10 negative, it was noticably soft, even without a comparison print.
I much prefer using the 240mm because of working distance. I rarely print bigger than 16x20 and haven't printed larger than 20x24 in years. If anyone is interested in a 300mm Rodagon, I'm willing to sell mine.