From an aerodynamic aspect, how do partial flaps and full flaps compare for gusty approaches?
I’m not sure when it comes to large aircraft, but when you select partial flaps or opt for a no-flap approach and landing, it results in a higher speed on approach and landing.
If you then break down the wind components in vectors, the cross-wind component becomes relatively smaller, so it is as if you have less cross-wind and don’t need to have such a large cross-track angle upon landing (less crab) or less cross-control when touching down. Even though the effect is small, it is noticeable.
You can compare it with a small single-engine piston trying to stay on course with 30° of crosswind at 100 kts needing perhaps 15-25° of cross-track angle while a fighter flying at 450 kts only needs 3-5° or so under the same conditions.
It varies from airframe to airframe, though often times OEMs recommend partial flaps and a gust factor be added to Vref in order to ensure positive control all the way through the approach and roundout - at least for light aircraft.