Byrna
My judgement is (having flown the 737, A320 family and the 747-400) is:
747-400
1. Has more momentum, therefore 'rides' the bumps with less deflection
2. At average weights, has a higher final approach speed (typically 150+kts), and therefore needs to lay off less drift
3. Has a higher wing loading (see 1 above)
4. Has better ground effect helping the flare.
5. The pilots carry out fewer landings and have usually just completed a long duty period which can counter 1, 2, 3 and 4.
6. Higher risk of pod scrape
737-2/3/400
1. Lower wing loading, therefore easily bumped around (esp the -200)
2. -200 has lowest landing speed (along with A319) and therefore greatest amount of drift
3. Not much ground effect
4. Pilots in very good practice
5. 2 engines mean that the risk of pod scrape is low
A320 family
1. Not much difference in speeds and hence drift to the 737 family
2. A320/321 and 737-400 have similar approach speeds, and low pod scrap risk
3. Pilots similarly practiced
4. Airbus FBW has totally different handling characteristics to 'conventional' aircraft which can work for and against. Pilot Induced Oscillation (PIO) is possible causing some approach destabilisation.
Personal preference, well they each have their merits, but for controllability the 737-200 can't be beaten, as a modern workhorse in shorthaul the A320 is unrivalled, but the 747-400 is the Queen of the Skies.