When Airbus introduced the
A310, it was the aerodynamically most advanced wing in transport aircraft design, obviously much better than any existing Boeing design at that time. For modern Boeing design, there is not much difference to modern Airbus design, both are at comparable level of aerodynamic performance.
Anyway both companies follow a sligtly different optimisation idea, Boeing wings have a little more sweep. This improves high speed performance by reducing transsonic drag. Therefore Boeing aircraft cruise a little faster. On the other hand wingsweep is bad for high lift performance, especially the outer wing is not able to work at high CL. To compensate for this Boeing wings have to use more sophisticated trailing edge devices like multiple slotted flaps.
If you compare the
B777 wing flaps to the
A330 design, you see the large gap between inner and outer flaps at the engine position for the Boeing, while the Airbus flap is continous. To have the same overall high lift performance, the flaps with ´engine window´ need to have better performance than the continous, therefore they have to be slotted.