I know I had a lot of trouble at first taking them down, so here's the best way:
Before you take one on, use the splicers if they are around. Enrage them and they will do some damage to the Big Daddy.
Hack any turrets or bots you can. When he goes crazy on you, the turrets will attack and draw his attention away.
Have your shotgun out with electric buckshot equipped. Unload all 4 rounds a second between each shot to keep him shocked and immobilized.
Finish him off with the grenade launcher.
As soon as you use all 4 electric buckshots, click your RB and launch a grenade.
That will take down any Big Daddy, Rosie or Elite Bouncer you come across.
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