Delta Compare is an advanced feature which helps the player to compare their inventories. Through filtering out all mutual Badges, it helps to figure out which missing badges the other player has and which of the on badges the other player is missing.
On the left side of the Badge, you see how many of this type you have in inventory. On the right side, how many the other player has.
Tap on one of your owned and you will see a list of all of them. Tap on one and you get the known Badge Detail View.
To use this feature, the other player has to share his inventory. This can be done via Common Quadrants menu using the following button: