Should I get arkham asylum or arkham city?

I'm only interested in buying one. I know arkham city is newer but which one is better and worth the money? Also would i be confused about the story if i skip arkham asylum?Should I get arkham asylum or arkham city?
Both are great games. I have not yet finished Arkham City but I don't think you would be confused if you got Arkham City before Arkham Asylum.

However it may be best to get AA first.Should I get arkham asylum or arkham city?
Batman: Arkham Asylum is third-person Action-Adventure game that delivers an authentic Dark Knight experience rooted in an original and engrossing story as well as a combination of melee combat, stealth, investigative and speed-based challenge gameplay. A sequel to 2009's Batman: Arkham Asylum, Arkham City features the full range of classic enemies seen in the previous game, in addition to Catwoman, who is a playable character and has her own storyline in the new release. Additional features include: a range of new gadgets, an increased number of possible melee opponents and a range of movement options for Batman that include leaping, sliding, gliding and the grapple hook.