If you look hard enough on the Point Prometheus level you can play as a Bouncer Big Daddy.
The only type of Big Daddy you can play as is a Rosie Big Daddy. The protagonist Jack Ryan must make this transition to complete the game.
If you kill 500 Spider Splicers with the Wrench you can play as a Big Daddy Assault: a purple and orange Rosie Big Daddy with giant AK-47's for hands and Tank tracks for legs. If you kill 500 Houdini Splicers with the Wrench you can can play as the Big Daddy Carbine: a green and red Bouncer Big Daddy with giant M4's for hands and 4 wheels for legs.