The lower of the two images is not as sharp. I would have to see more to know for sure what the cause is, but I think this is just inherent in the lens design.

Although the settings used were the same, there are a lot of differences in the lens design.  The key difference here is that at f/5.0 the 35mm is [stopped down][1] a full 3 stops from it's maximum aperture, whereas the 18-55 is [almost wide open][2].  This makes a big difference in the sharpness, because in general, a lens will be sharper when stopped down a bit.  You might want to try finding the "[sweet spot][3]" of your 18-55 (I would guess around f/8) and see if you notice a difference.


  [1]: https://photo.stackexchange.com/questions/9610/what-is-the-meaning-of-stopped-down
  [2]: https://photo.stackexchange.com/questions/6177/will-using-a-lens-at-max-aperture-wide-open-result-in-poor-images
  [3]: https://photo.stackexchange.com/questions/2917/how-do-you-find-out-the-sweet-spot-of-a-lens