I got 2/3rds thru a hard mode Arkham Asylum playthru before stopping. I beat it many years ago, and imo, Arkham City does everything better.
In Asylum, I got to the part where you have to destroy Poison Ivy pods that shoot auto tracking plant missiles. Before this downward spiral in quality, its felt like:
Battle area
Stealth area
Batle area
Stealth area
Stealth area
Scan objects
Cutscene
Story progression and XP unlock new abilities and content. Exploration away from the main goal in Asylum nets you Riddler stuff, giving you xp and side content.
Metroidvanias reward exploration in more drastic, better ways. New weapons that can be op or have a unique moveset. You can try to break the game using gear and exploits, something I don't know if possible in Asylum.
The Arkham games as a series are character action vehicular stealth games.
Arkham City has a similar forumla, but it starts closer to Asylum's entire skill tree for Batman's abilities, almost from the start of the game. The more cohesive open world map and art design helps a lot too.