This is TWO Servitors in one! They're not separate. Though they'd be fine separate, they do much better together.
Booker is a serious, occasionally self-loathing man. He's done many cruel things in his past that he deeply regrets. One of the biggest things that plagues him most is giving away his daughter in exchange for his gambling debts being wiped clean. He was in the army, and is an ex-Pinkerton agent (who was, at the time, notoriously violent), so he's more than capable of handling himself in fights, if the need arises. He is imperfect, but he can be caring and protective when he likes you.
Booker's companion, and unbeknownst to him for a large amount of time, long-lost daughter, is Elizabeth. He is protective of her, and though she can be stubborn, and doesn't always agree with his way of doing things, they work together quite well.
Booker is fully capable of protecting you, and will be a helpful ally. He can help remind you to think before doing something you may regret.
Elizabeth is a sheltered young woman. She is very intelligent, though lacks life experience. She has a free and almost childlike spirit. She used to greatly dislike killing, but she's reached a point where if it needs to happen, she can accept it. Surprise talent: can sing.
She can open up tears to other "realities" (astral locations) to suck in enemies or negative energies.
Elizabeth is Booker's occasionally hesitant companion, and long-lost daughter. Though she doesn't always agree with the things he does, he's proven he cares about her, and she sticks with him.
Elizabeth is can take care of herself quiet well, and she will be a kind friend. She might just be able to give you insight into some of your "what ifs" as well.