In uncountable|lang=en terms the difference between aggressiveness and hostility
is that
aggressiveness is (uncountable) the state or quality of being aggressive while
hostility is (uncountable) the state of being hostile.
In countable|lang=en terms the difference between aggressiveness and hostility
is that
aggressiveness is (countable) the result or product of being aggressive while
hostility is (countable) a hostile action, especially a military action see hostilities for specific plural definition.
As nouns the difference between aggressiveness and hostility
is that
aggressiveness is (uncountable) the state or quality of being aggressive while
hostility is (uncountable) the state of being hostile.