Is the Canon EF-S 15-85mm f/3.5-5.6 IS USM Lens sharp? This page visually answers that question. Shown above are 100% crops from a lab-captured 15mm f/4.0 test image. Observe the contrast and resolution of these results.
Is the Canon EF-S 15-85mm f/3.5-5.6 IS USM Lens set to 15mm f/4.0 sharper than the Tamron SP AF 17-50mm f/2.8 XR Di II VC LD IF Lens set to 24mm f/2.8? The image quality comparison above also answers that question. Switch between the results to see the sharpness differences between these lenses.