Apparently some whales feed on the giant squid. And they obviously have such superior speed that they can choose to attack or evade. Whales have been seen with the tentacle marks on them. No way of knowing how often the whales lose.

http://seawifs.gsfc.nasa.gov/squid.html This was only URL I could find. It does say the squid are prey. No details, alas.

Squid species vary greatly in size. The common squid of the east North Atlantic coast is 30 to 45 cm (12 to 18 in) long, and the giant squid, at least 18 m (60 ft) long, is the largest aquatic invertebrate. It lives at depths of 300 to 600 m (985 to 1970 ft), where it is the prey of sperm whales.



"Squid," Microsoft(R) Encarta(R) 98 Encyclopedia. (c) 1993-1997 Microsoft Corporation. All rights reserved.