JBilgeRat is working on a song about a merchant vessel with only a Naval Auxiliary gun crew and a six inch gun sinking the Scheer. Both vessels sank. It is, as far as I know, the only documented example of a merchant vessel sinking a major ship of war.

On the question of who lost more men, both groups lost a lot of sailors. Arguing over who suffered more is like [sorry, but the only analogy I can come up with is very uncomplimentary. Out of respect for both groups, I'll leave it out.]