Is the Canon EF-S 55-250mm f/4-5.6 IS Lens sharp? This page visually answers that question. Shown above are 100% crops from a lab-captured 200mm f/6.3 test image. Observe the contrast and resolution of these results.
Is the Canon EF-S 55-250mm f/4-5.6 IS Lens set to 200mm f/6.3 sharper than the Canon EF-S 55-250mm f/4-5.6 IS II Lens set to 70mm f/5.6? The image quality comparison above also answers that question. Switch between the results to see the sharpness differences between these lenses.