Is the Canon EF 75-300mm f/4-5.6 III Lens sharp? This page visually answers that question. Shown above are 100% crops from a lab-captured 135mm f/4.5 test image. Observe the contrast and resolution of these results.
Is the Canon EF 75-300mm f/4-5.6 III Lens set to 135mm f/4.5 sharper than the Canon EF-S 55-250mm f/4-5.6 IS II Lens set to 250mm f/8.0? The image quality comparison above also answers that question. Switch between the results to see the sharpness differences between these lenses.