What is this difference between these two 4 pole (3 phase) GFCI breakers?
I see what's going on here.  

You have a 3-phase RCD, but  your supply is only single-phase.

Let's look closer at that picture. 



The top is the line side.  The orange wire is the real incoming hot.  The grey jumpers take the hot wire over to the other 2 phases.  

What this brightened picture shows clearly is that the load side of the breaker is wired as 3 phases.  The apartment wiring takes 3 conductors, one off each phase, to be distributed to various apartment loads.  So the apartment is "3-phase-ready" even if the service is not (yet) 3 phases.  

This is a danger area.  Each phase could pull 40A before any breakers would trip. I doubt that gray jumper is rated for 80A.  I also doubt the orange wire is rated for 120A.  Maybe it is downline of other breakers. 

Your new RCD won't trip because there's no voltage difference

And therefore no current flow.  All phase (LINE and LOAD) conductors, all 6 of them, are at the same voltage potential. As such, there is no current movement through the TEST circuit.

So the upshot is, this device's Test functionality will not work here.  If your house is grounded, you can use external GFCI testers. 

30ma isn't that great for human protection anyway

It's certainly better than nothing at all, but 30ma can be lethal for humans, and will definitely stun.  That is the motivating factor behind 5 ma protection on US devices; stunned people drown or fall, so a stun is the same as a kill.  Generally Europe does RCD for parallel arc fault detection.