This really isn't a fair test of the lens. For one thing, the apertures are different, you've used different focal lengs and both images are under-exposed.
To get a good technical comparison, try my home-brew lens "resolution" test; do this for both lenses and compare the result, you should notice a major difference in the corners, especially wide-open:
In the meantime, I suggest a home-made lens resolution test: Use a LASER printer (NOT inkjet) to completely cover a sheet of paper with 12pt upper-case 'X's. Using a tripod, level and square, position your camera such that it is within the minimum focusing distance (eg, if your lens will focus as close as 12" then use, say, 14") and ensure that the sheet of paper is exactly square to the lens axis. Use your lowest native ISO, and supplementary lighting if necessary to ensure a correct exposure.
Focus on the centre on the of sheet of paper and make an exposure wide open, followed by a series stopping down by a couple of stops each time. Then, examine the centre, and edges at 100% and compare sharpness. Even wide open, at the edges, the characters should be legible. This will give you a good idea of whether or not there is a problem with the lens (It's unlikely, but it can happen) and just how it performs at different apertures.
Don't forget too that your kit lens isn't a bad lens; there are still hundreds of thousands of dollars worth of optical design in it. At the size image posted here, you'd be hard-pressed to tell the difference between the image shot with your $250 18-55 and my $2000 24-70.