If I'm not mistaken they both use the hot fix, maybe you made a mistake by thinking the gray out part are using a difference version. when it could be just a game being played.
Here is a example.
The
red arrow show the game is being played
The
green arrow show that the game can be join
The
yellow arrow show the game is using a difference version, if is the same version you would not see the patch version you see there.
Use this that i mark in the
blue arrow this will remove the game that are being played from you screen and show only the one that are open to join.
Also in the Victory day version you would not be able to play in all the co-op mission as is only have 3 co-op mission than the full version but for everything else is the same.