In Airbus, Vx is "green dot" speed (minimum drag speed).
Vy is CI=0 in some texts. In others they state that flying at rough air speed you are close to Vy.
Vy happens to be, according to the above, much much faster than Vy.
With the nowadays low cost indexes, ECON speed is not far from Vy.
Every time I am instructed to "expedite climb" I don't know if they want me to climb soon in time or in distance. When they say "Be level or pass FL XX by position ZZZ" then it is clearly Vy (min drag)."
Vx is also used after take off with, say, a north heading and your route is to the south. There is no point in flying miles north, so you climb as steep as possible until you reach the turning altitude or until ATC tells you to turn. This does not apply if the SID is just a sequence of geographical waypoints. In this case you cannot alter the total number of miles to be flown.
But in a "at 6,000 ft turn right to XXX" departure, climb at Vy, since every mile you fly in the non desired direction will be flown twice (one going and one coming).
Vy can be used to clear a cloud or turbulent layer, if it is not far from turbulent speed (which is not in the 320).