Hello amf99,
the SD card on the right (in the box) is the one, which works. The one on the left doesn’t. The problem is: They are both the same type!
Now, I really think that I may have confused, what I actually flashed on the working SD card. I was absolutely not aware, that preparing an SD card for the BeagleV-Ahead was such a big deal. And I also tbh. did not so much know what I was doing: I actually just compiled the u-boot and afterwards flashed different binaries in a trial-and-error manner onto the SD card, untill it worked. Then I cared more about the annoying button.
What I could do is obtain the image from the working SD card, e.g., via dd and then try to identify from that which binary file was flashed onto the SD card. However, I would need help for that, i.e., which tools to use for something like that, because I don’t know how to do this. Also if there are tools to get some hardware specifics of the two cards, I could use them and drop the output here. If someone is really proficient with this stuff, I could even send the SD card to that person, given, that I get it back eventually.
The image also contains the only serial interface I had at hand, which worked with the BeagleV-Ahead (see also How to see boot messages on uart). Unfortunately it stopped working 
So I have to get another one. So, with regards to testing, my hands are a bit tied.
Best regards,
Kilian