Only air missiles trigger the @BATTERY popup, and it doesn't appear that the defense factor is enhanced v. ground missiles. Didn't realize that the test would be so straightforward.
Edit: oops! I had to interrupt my reply above to keep the pasta pot from boiling over. Didn't see your reply St Leo. I think it goes as follows when air units attack cities.
Air units attacking fighters trigger the @SCRAMBLE popup. (x2 v fighter, x4 v bomber). Don't know if the defending fighter's domain is important.
SAM improvement triggers @BATTERY if the defender is not a fighter. (x2)
SDI improvement triggers @BATTERY if the attacker is a (air) missile. (x2)
SDI and SAM together trigger @BATTERY2 if the attacker is a (air) missile. (x4)
Don't know how AEGIS works in combo with any of these.