Is the Canon EF-S 18-55mm f/3.5-5.6 IS II Lens sharp? This page visually answers that question. Shown above are 100% crops from a lab-captured 24mm f/5.6 test image. Observe the contrast and resolution of these results.
Is the Canon EF-S 18-55mm f/3.5-5.6 IS II Lens set to 24mm f/5.6 sharper than the Canon EF 24-70mm f/2.8L II USM Lens set to 28mm f/5.6? The image quality comparison above also answers that question. Switch between the results to see the sharpness differences between these lenses.