The Rumbler type of Big Daddy in this game is a revision of the SLOPRO Big Daddy which was cut from the first game. The initial concept for the character had the shoulder mounted cannon as seen in BioShock 2 but instead of being able to set up mini turrets, the SLOPRO held a massive hook which it used to perform lethal melee attacks.
Series creator and writer of the first BioShock and BioShock: Infintie Ken Levine was not involved with BioShock 2. This led to some contradictions to the previously established continuity. For example BioShock 2's antagonist Sofia Lamb is said to have been a big political figure in Rapture and almost overthrew Andrew Ryan of his power, but it's specifically said in the first game that the only person to ever challenge Ryan's power was Frank Fontaine.