I guess you can't do both at the same time! So which one should I have in my swing?
Both but not at the same time.Twistaway first half of the backswing and then the quarter turn to finish off the backswing and into transition.This is my preference but you can twistaway all the way to the top,however,you will end up with an arched left wrist and depending on the length of your backswing,across the line as well.Some people play well from this shut position so feel free to experiment.
What you don't want is the quarter turn to happen in the takeaway which leads to popout and a very flat backswing.You want to flatten it with with the quarter turn as you reach the top of the backswing and into transition.May feel weird at first because in essence you are opening up the clubface to start your downswing which might raise a few eye brows in this part of the woods.
Another way to think of the twistaway is just don't quarter turn at all during the backswing.This might feel less awkward for most people.