You're talking about 2 completely different things, PMP is a certification, while MBA is a degree. If you still want to compare them difficulty wise, then I'm certain that the MBA is much harder than the PMP (I have both). Here's why:
- MBA is for at least two years if you're full time and if you're doing it in a decent university (some, shall I say, non-reputable universities let you do it in one year instead), while the PMP can be done in a month or two.
- The MBA is comprehensive, and it encapsulates a lot of management concepts, including project management. The PMP is only about project management.
- Studying for the MBA is hard, you never have time to rest. There's always a lot of pressure. The PMP, although not easy, is not that hard, and you can take it whenever you're ready (you're not bound by time restrictions).
- Some teachers for the MBA are quite tough, and few of them are sometimes against you graduating. On the other hand, if you're taking a course to prepare for the PMP, the teachers are very soft and helpful. There's a substantial difference between MBA teachers and PMP teachers (ask anyone), the former want you to fail and only succeed if you really have the necessary management skills, while the latter want you to succeed at all cost.
One last thing, judging from your question, I'd go with a PMP blindfolded.