Becky, there are all sorts of combinations of effects that might be responsible. Looking at your pictures, is there a difference in mulch between the two areas?
It also happens with other plants that seedling resistance and adult plant resistance to rusts can be different, I don't know if that might apply to daylilies.
Like Judy, I also wondered if the leaf trimming might have made some difference. Bear in mind a leaf or part of a leaf can have rust inside that hasn't sporulated (produced spores) yet in which case you can't tell it's there. It does look like in one of your pictures that the leaf tips are affected, I think.
Regarding stress, that's a rather controversial topic. There are some authorities who believe that stress reduces rust rather than increases it. Others say that might only be the case at certain stages of the disease. The logic would be that since rust is one of the few fungal plant diseases that needs living tissue to survive and reproduce, it will do "better" on healthy foliage. Most fungal diseases of plants can also persist on dead and dying foliage but not rusts, smuts or powdery mildews which are considered "obligate parasites". Some daylilies have a reaction to rust that causes the whole or part of a leaf to die. That might make it appear that the plant was more stressed.
It's also possible that your two beds, although fertilized the same, do have different nutrient status (from differences in the native soil), and that can affect rust severity. I wouldn't have thought that would make such a big difference though unless there is a dramatic difference in the nutrient balance.
Edit: forgot to mention, is there a difference in plant spacing between the beds (including non-daylily)? The trimming could also have created more air circulation as well. Another thing again is temperature related resistance genes, if such exist for daylily rust.
