At what F/stop? The 18-55 is a remarkably sharp lens stopped down a stop or two. It's one of Nikon's sharpest. Its only limitation is that it is slow. In good light at f/8 it's doubtful you would notice any difference between the two at any focal length in the zoom range. The 18-55 might have a tiny bit more distortion, but it isn't much and it is easily corrected in PP.
Photozone sharpness tests... It's comparing DX to FX, so the resolution numbers don't apply, but you can get an idea from the chart. The irony is that the 18-55 is Nikon's cheapest kit lens!
If you can't get super sharp results with the 18-55 in good light, odds are it's your technique, not your lens. Perhaps the difference in sharpness you noticed was due to motion blur from having to shoot at too slow a shutter speed in low light. Upping the ISO a bit would fix that. With current camera bodies that can shoot in the dark, fast apertures are becoming only necessary for bokeh effects, not for speed as much.
Edited by bigshot - 2/15/13 at 12:03pm