I've timed them, and the pump is faster in trained hands. Also, once it runs empty, it can be loaded/fired faster (via the ejection port) than an auto.
At least my pumps (870, and 1897's are faster than my 1100's and 11-87's).
For most pumps, all you have to do is drop a round in the port, close the action and fire. With an auto, you have to drop one in, then release the action, then fire. At least 1/2second faster with the pump.
Pump is more reliable.
Pump handles much wider variety of ammo.
Pump is cheaper.
Pump has no O-rings to dry out.
Pump has no gas ports to keep clean.