While I don't disagree; I will point out that depending on the state of the sea and the ability to see your victim; remaining under sail might be better. If you are sailing upwind and you drop to a beam reach you are parallel to the COB. If you turn around and motor or sail directly back you might either be to the left or right of the COB or not in a position to motor directly to them without running them down.
In heavy seas a sailboat is more stable under sail; so keeping the sails up and using the wind might be safer for keeping yourself and other crew aboard if you are doing the SAR.
In calm waters or inland sailing it might be better to motor to the COB. If I had a COB situation the engine would definitely be running and ready to assist me in getting back to them.