This was definitely a massive leap in scope and a further refinement of the Arkham series gameplay. The story was great and the city was really fun to explore. The improvement to combat and abilities were really fun when I remembered I had them and helped with that awesome feeling flow of the first. The new movement abilities make traversing the open world really fun and fluid. Just off a pure gameplay level a complete step up.
That said I think kind of preferred Arkham Asylum. This is completely a preference thing but I liked the streamlined experience Asylum had a little more, it just felt more focused. It was designed like a 3D metroidvania, a genre I'm a bit of a sucker for. Lastly I thought the atmosphere was done better in Asylum. I'm not saying City is bad or anything because on an objective level it improves the franchise in almost every way and is a genre defining game, it's just preference. Both games were amazing so far, can't wait to play Arkham Knight.