AA works for many, but for Christians, replacing the term "higher power" with Jesus Christ makes recovery more meaningful and resonant with truth and Faith. For many Christians, joining a Christian 12 steps group or Christian rehab just makes more sense.
I don't know if recovery statistics show that Christian programs of recovery are more succesful than secular rehabs - but I do know that when Christian Rehabs work, they teach sobriety, but they also teach happiness.