No poll?
Anyway, I think the answer to which is better is "Yes". No, seriously.
Batman Begins and The Dark Knight are great films and I enjoyed both. The characters, the setting, and just the way the movie felt were great. You could almost see it happening in real life. Of course, Heath Ledger gave one of the best performances as Joker in Batman's history. All in all, Nolan's films have been great and gritty adaptions of Batman. A work of love if anything.
Arkham Asylum and Arkham City really make you feel like Batman. You become a serious badass who can stomp on 20 guys at once. Batman goes toe to toe with Bane, Killer Croc, and Solomon Grundy and it feels natural. Nothing beats gliding over the city streets and getting the drop on goons or slowly eliminating groups of armed guards without being seen and listening to them freak out and Batman picks them off one by one. There have been so many times playing the games that all I could do was say "Are you kidding me?" They're works of love, too.
I think the main point is this. When the people making the game or movie truly care about the character and the content, it flourishes. The reason we can gush about these great works is because the guys and gals making them wanted to make the best work they could.
I'm still waiting for The Dark Knight Rises. I wonder if we can look forward to a new Rocksteady game in the not too distant future and what it'll be.