Is the Nikon 55-200mm f/4-5.6G AF-S DX VR II Lens sharp? This page visually answers that question. Shown above are 100% crops from a lab-captured 105mm f/4.5 test image. Observe the contrast and resolution of these results.
Is the Nikon 55-200mm f/4-5.6G AF-S DX VR II Lens set to 105mm f/4.5 sharper than the Nikon 55-300mm f/4.5-5.6G AF-S DX VR Nikkor Lens set to 300mm f/5.6? The image quality comparison above also answers that question. Switch between the results to see the sharpness differences between these lenses.