It was the Super Étendard that fired the Exocet missiles that got some British warships. The Argies sent their Mirages to challenge the Harriers but after the Brits bagged a few they gave up. Interesting game of cat and mouse when the Mirages tried to challenge the Harriers. The Mirages tried to get the Harriers to go high but the Harriers stayed disciplined so when the Mirages dropped their altitude the Harriers were at an advantage.
In air combat -
UK Harriers 0 lost - Arggie Mirages 1 lost
For all aircraft - flying and in combat, air-to-air -
UK Harriers 5 lost (all due to ground fire/missiles) - Arrgie planes 21 lost due to Harriers (with an additional 19 lost due to ground fire/missiles)
I think that clearly defines the winner of the war in the air.