Congrats for those great offers you received! In the end it matters what you want and what your long-term goals are. Do you want to work in consulting in the short or long term?
If it was me, I would probably choose the DAX company. It's a trainee which you could see as a disadvantage, but I think it gives you good possibilities to see different parts of a company and good experience to enter consulting later. After the trainee plus maybe a few years of experience, I would probably try to apply again to MBB as an experienced hire, as that is my long-term goal. Another option could be to work at the big 4 and then also apply again to MBB. For me personally, I would prefer the trainee, because it offers more variety I think.
No clue if this helps, but you asked which one we would choose, so there you go ;)