This causes the 2 creatures to compare power, with the creature with the lowest power being put into the graveyard. If both creatures have the same power, both creatures are put into the graveyard. If an effect prevents the creature with the lower power from being destroyed, both creatures remain tapped. The only exceptions are Win All Battles abilities where a creature with lower power may destroy a creature with higher power in a direct battle.
A battle does NOT occur when an unblocked creature attacks the opponent in order to break a shield or win the game.
701.13a To battle is to compare the powers of the battling creatures and to see which one wins or loses the battle. Creature with the highest power wins the battle, while the creature with the lowest or the same power loses the battle.
701.13b Creatures that lose a battle are destroyed.