Have flown both B737 and A320 and landed both in limiting crosswinds. There is nothing special about landing the A320 in a crosswind compared to the B737.
I dont like the phrase "kicking" off the drift. I have never had an occasion where it was necessary to kick the rudders. I think the phrase "straighten (or align) the a/c with the runway track" is far more appropriate. The further effect of rudder is and always has been roll in any a/c which I have encountered. Therefore as you apply the rudder you need to apply opposite aileron to keep the wings level. If you are going to make any mistakes apply too much aileron rather than not enough.