Filp the swiches to see that the current will change when the number of diodes changes and that that is not the case for the current mirror.
The three diodes on the left have a current limiting resistor. The reason why the three diodes on the right are lit more brightly is because their current is limited by the two transistors and the resistor across vcc and collector of the transistor in the middle.You can say that the diodes on the right are connected to ground through the transistor on the right and don't have a current limiting resistor so they allow as much current flow through them as the transistor allows, there for you can set the maximum current by adjusting the resistor value resulting in setting the reference current.
