For Arkham Asylum, If you look at other media that was released with the game like comic books that tied in with the game and the posters, Batman costume is Dark blue. I believe the Blue is meant look black in low light condition (for Stealth) but in reality it is blue.
I have the "Dr penelopeYoung" Journal that came with the AA Collectors edition, they have pictures of all the Rogues and Batman. They are not screen captures, but rather color drawings in the same style of the comic book. In there you can clearly see batman suit is blue.
I believe Rocksteady always meant for the suit to be a very dark/greyish Blue for both Asylum and City, based on the other material that were released alongside with it.
However I have played this game on both Xbox360 and PS3 and on the xbox the Blue was more evident, on the PS3 it did look very much like black... maybe it was my tv settings as well (different tvs on each system).