I'm with Chesty and ManaAda here.
On the 737 (200 to 800 variants). Crab until shortly before touchdown and then squeeze the drift off applying aileron to keep the wings level and erring (if that is the right word) into lowering the into wind wing a little. Worked well in very strong crosswinds with plenty of rudder and aileron left. That was how I was taught and it seems to work for me. Ditto the 757.
The 777 was a somewhat different matter as we were taught the wing down method but also that crab was acceptable. Aiming to keep the main gear on the centreline was required. Never did any limiting crosswind landings as at that time I was an F/O.
The A320: I once had difficulty in keeping the into wind level on a strong crosswind despite full into wind sidestick (I was reasonably new to type). Talking to some A320 old hands who told me that the drift needed to be removed early in order for 'the system' to catch up. Not sure about the truth in that. The Bus always held some 'mystery' for me but many others loved it.
The final approach and landing, whether crosswind or not, and regardless of type, should always be carried out visually.
Regards
Exeng