MSF in Europe or MBA later on to avoid being pidgeonholed?

Hi everyone, I'm currently an incoming summer 2026 analyst for PubFi at a BB, though I've realized that my current internship isn't exactly what I want to do long term. PubFi is also a relatively more niche skill set, and I'm aware exit opportunities aren't as stellar. I'm a student from a non target state school with a reputation for partying, and its a blessing I was able to secure this internship in the first place (I had a 3.5 at the time of application and acceptance, currently have a 3.7) so beggars can't be choosers, but I was wondering if pursuing a Mfin would be a better option post grad to help account for my current schools lack of credibility, as well as my fear of being pigeonholed into pubfi. I'm aware that Mfin tracks are shorter abroad than here in the US, and with the amount of family I have there I wouldn't mind even relocating permanently if given the opportunity. On the other hand, I'm aware that most tend to say and MBA is generally considered the better path.