Is the Canon EF-S 55-250mm f/4-5.6 IS II Lens sharp? This page visually answers that question. Shown above are 100% crops from a lab-captured 55mm f/4.5 test image. Observe the contrast and resolution of these results.
Is the Canon EF-S 55-250mm f/4-5.6 IS II Lens set to 55mm f/4.5 sharper than the Sigma 18-200mm f/3.5-6.3 DC OS Lens set to 18mm f/3.5? The image quality comparison above also answers that question. Switch between the results to see the sharpness differences between these lenses.