So, I bought the sets myself...
The answer is not quite a simple as I thought when I asked the question, so a detailed answer follows.
About the new trains
While the old trains are black, the new trains are dark blue. The light in the front is redesigned. The light sensor underneath looks brighter. The speaker seems to have a better sound quality. The speed of the train is changed (but that is another topic on itself I might post about later).
The Action Bricks
| Action Brick |
Existing / New |
Functionality with old trains |
Functionality with new trains |
Picture |
| Red |
Existing |
Stops the train |
Flashes red, plays a sound, the train backs up a bit, drives ahead faster than usual, continues ahead |
 |
| Blue |
Existing |
Stops the train for a few seconds while it plays some sounds, drives along |
No effect |
 |
| Green |
Existing |
Reverses the direction of the train |
Flashes green, plays a sound, reverses the direction of the train |
 |
| White |
Existing |
Turns the light on/off |
Flashes white, plays a sound, drives along. The train drives forward no matter the direction it had before. |
 |
| Yellow |
Existing |
Makes the train play a sound |
Plays a sound, flashes yellow |
 |
| Blue |
New |
Stops the train for a few seconds while it plays some sounds (as existing blue brick) |
Makes the train go a bit back and forth, flashes blue, plays a sound, the train drives on |
 |
| Dark green |
New |
Reverses the direction of the train (as the existing green brick) |
Slows the train down, flashes green, plays a sound, continues at normal speed. The train drives forward no matter the direction it had before. |
 |
| Light green |
New |
No effect |
Stops the train, flashes green and plays a sound |
 |
| Orange1 |
New |
Turns the light on/off (as the existing white brick) |
Stops the train, flashes red and plays a sound |
 |
| Orange2 |
New |
Stops the train (as the existing red brick) |
Stops the train, flashes red and plays a sound |
 |
| Yellow |
New |
Stops the train (as the existing red brick) |
Makes the train go a bit back and forth, flashes yellow, plays a sound and stops the train |
 |
| Purple |
New |
No effect |
Plays a sound, flashes purple, continues driving for a while in this state. The train drives forward no matter the direction it had before. |
 |
Effect on each other
While the existing trains read one action brick at a time and thereby do not affect each other, the new trains are different. For instance, when the yellow action brick makes the train play a sound the train will not respond to any subsequent action bricks it drives over while the sound is playing.
Changing behaviour
I have noted that the effect each action brick has is not always the same. For instance, usually the red brick makes the train drive fast for a bit, but on rare occasions the train stops instead. I do not know if this is a feature or a bug.
The App
I have yet to test the app, but will update the answer once I do try it.