The evidence for squid / blue whale battles comes from scars on blue whale-- living blue whales.. so sometime the whale wins.. and since whales can remain submerged for several hours.. (at least 1.5 hours for small whales, and maybe as long as 3 for large ones). its not as if the have to rush the battle..

AMNH has a big blue whale hanging from a ceiling-- and not far away-- it has a giant cuttle fish-- i'd but my money on the whale most of the time..