Shuttle Launch Postponed To July 4th
Of course, the shuttle can take a much, much larger payload than anything else currently available (I think).
More importantly, the Shuttle can return payloads and experiments to the ground. The Soyuz module has very little space to return payloads. Progress is destroyed during re-entry, as ESA's ATV will be.
In addition the Shuttle connects to ISS using the US docking port allowing the of transfer large rack-sized payloads into ISS. For example this mission will deliver the MELFI rack payload to ISS (a freezer capable of -80C) developed by EADS through ESA for NASA. For more information on MELFI see the ESA fact sheet (pdf).