The Contenders: Immortal Human vs Space Monster.
When: Torchwood: Children of Earth "Day Five" Season 3 Episode 5.
The Battle: The 4-5-6 was a particularly gruesome space monster hailing from a neighboring galaxy, but instead of borrowing a cup of sugar, they wanted a few million children as a "gift." Unable to just snatch up the required kiddies, The 4-5-6 use a special frequency to communicate through the children of Earth, having the kids repeat "We are coming!” (mostly as a scare tactic). It is quickly revealed that The 4-5-6 want the kids because their young biochemicals get them higher than space weed.
While secretly hoping The Doctor would come save them, what was left of Torchwood set out to find a way to destroy the invader. They eventually deduce that they can reverse the frequency back on The 4-5-6 through a child, thereby creating a destructive feedback. The process would surely destroy the monster, but it would also painfully kill the child as well. Sadly, the only kid nearby was Captain Jack's own grandson Steven, who he tearfully sacrificed to save the world.
Winner: Nobody