Ken Levine confirmed on his Twitter that the Rapture in Burial at Sea is the exact same, prime Rapture that we play in as Jack in BioShock. That being said - there are certain characters we need to account for that were featured in Burial at Sea. Namely: Atlas, Sander Cohen, Frank Fontaine, Andrew Ryan, Yi Suchong, Jack, Jeremiah Fink, Daisy Fitzroy, and others if you can name them.
Their actions in Burial at Sea occurred before the events of BioShock/BioShock Infinite. So their actions should be chronological with what they do. For example:
Atlas's page should include his history, his actions in Burial at Sea, and THEN the events of BioShock. Not his history, BioShock, then Burial at Sea.
Daisy should get a notice too. That before she went on to threaten the boy - she was actually visited by the Lutece Twins where she had no intention to harm the boy but they made her in order to further her cause.
One more thing. Elizabeth in Burial at Sea is not an alternate version. It has been confirmed that she is the same, prime Elizabeth from BioShock: Infinite.