Speaking about -300 and on:
ENG 1 (EDP) is the main source for system A and the EMDP is the electric backup.
ENG 2 (EDP) is the main source for system B and the EMDP is the electric backup.
If you take a closer look at the hydraulic panel you see that the EMDP for the system A is named ELEC 2 and the B EMDP is named ELEC 1.
This is because the (electric) power for A EMDP comes from the generator mounted on ENG 2 and ENG 1 is the source for B EMDP.
This crosswiring ensure powering of hydraulic system A when you lost ENG 1 or system B when you lost ENG 2 through the electric powered EMDP from the other side without any switching. You have enough to do when you lost one engine ;-)