I preferred Arkham City to Arkhma Origins. AO has so many game breaking bugs, it makes you wonder how it passed the QA testing in the first place. Floors that disappear into the infinite black pit, Burnley Tower that cannot be escaped, Batman just refusing to interrogate "Bird" or enigma's informants after beating them, Batman and Bane refusing to fight each other at the very end boss fight (I had to re-start the fight 4 times just because of the bug), no "Crime in Progress" on Pinoneer bridge (so you cannot complete the challenges), etc.
Storyline wise, AC felt longer and more complex. The story develops gradually and keeps you guessing what enemies just as Joker, Strange, or Raj up to. It also had a pretty huge plot twist at the end. With AO, it tells you right off the bat, "Here is a list of boss fights you will need to do." That's pretty much it for the story. It felt short and a bit disappointing.
To give AO some credit though, I liked the larger map design (although I thought the buildings would be higher, since the devs put so much hype into how big the map and the buildings were). The voice acting was also very good, as always with Arkham series.