City's focus was to make the player feel like Batman. It did so by featuring stalking and gliding around a cityscape, stopping assaults of political prisoners, using smoke bombs, counter multiple attacks at once and being able to divebomb enemies from the rooftops. It was not trying to be a 3D Metroidvania "trying" being the operative word.
Asylum was focused because it was completely linear. It was not Zelda/Metroid-like beyond acquiring new items/abilities it's completely linear with the illusion of exploration.
Here's a post that explains why well:
The only advantages Asylum had over City were pacing (only achieved by being completely linear), basic story premise (which the game did not fully realize considering the linearity, high level of repetition and too few, too weak boss fights) and the Scarecrow encounters.
City still has the predator gameplay and is still structured similarly to Asylum what with gaining access to new areas as the game progresses, you're just able to get around without running through narrow corridors and encountering as many loading screens. It's not GTA with Batman. It's still a hub-type gameworld
Absolutely everything else is better in City. Boss battles, combat, gadgets, weapon dismantling, use of gadgets during combat, more predator options, actual puzzles for finding Riddler trophies, riddler hostages in Saw-type traps, actual Riddler encounter, grapnel-canceling and a non-cop out ending.
Play through Asylum again and pay attention to the repetition, how Bane is recycled as titans, the only boss fight is Poison Ivy, how you never even get the chance to explore and never have to figure out where to go, how terrible/out of character/"quintessential videogame boss"-style fight the final boss was and tell me how that beats what City brings to the table.
Even if you prefer more linear style games, how in the world is that more appropriate for Batman than traversing a cityscape?