There's the first type of Big Daddy you see, whose helmet sort of hangs lower and the 2nd type of daddy which is also the player in the 2nd game. What's the diff?
There are the rosies and the bouncers
the bouncers use the drill
the rosies use the rivet gun
there are also the delta series and the alpha series
the delta series is what you are, i'm not positive, but i think it is what the other big daddies are as well until you get to the end of the game and see the alpha series
the alpha series are more agile, they are faster and more flexible and such... they seem to die easier though, but they are more human like i guess
The Bouncers are the ones with the drills, the one on the cover of the game. The Rosies are the ones with the Rivet Gun. Bouncers can only hit you with the drill. The Rosies Shoot you. Thats pretty much it.
Bouncers are melee specialists, they also have more life. Rosies use ranged attacks and have slightly less life. In the second game, you are actually not a Rosie, you are the only survivor of the first prototype run of Big Daddies.
The player in the 2nd game is neither of the Big Daddies from the first game. In fact he is the first ever (or one of the first) Big Daddies, named "Subject Delta". In the first game, you encounter Bouncers, who are bigger, with more health and melee weapons such as a drill. The other type are the Rosies, who have the rivet guns, are more "thin" than the Bouncer, and have less health.