Is the Sigma 18-200mm f/3.5-6.3 DC OS Lens sharp? This page visually answers that question. Shown above are 100% crops from a lab-captured 135mm f/11.0 test image. Observe the contrast and resolution of these results.
Is the Sigma 18-200mm f/3.5-6.3 DC OS Lens set to 135mm f/11.0 sharper than the Sigma 18-125mm f/3.8-5.6 DC OS HSM Lens set to 125mm f/8.0? The image quality comparison above also answers that question. Switch between the results to see the sharpness differences between these lenses.