Monsters have a proficiency bonus calculated based off their challenge rating, whereas player characters have a proficiency bonus calculated based on their level. So then when i am possessing some other creature and i am using it's statistics, which would i use? 

On the one hand, me using the proficiency bonus in the stat block would mean that i would lower my own spell attack modifier and spell save DC if i possessed anything with a CR lower than my own level, which would already be almost every humanoid stat block by 11th level, and since my class levels have not changed i should still be using them to determine proficiency bonus

on the other hand, me having a higher proficiency bonus than my victim would mean that i'd need to recalculate saving throw and skill modifiers, and possibly even their attack roll modifiers, which could get pretty powerful if my victim was like a sahuagin baron or something, plus the target's proficiency bonus is undoubtedly part of the creature's statistics, a part of the creature's statistics that was not explicitly mentioned by the spell.

I’d assume if you’re possessing the creature, and took on the rest of its stats (such as wisdom, strength, etc) you’d also take on the proficiency bonus of the creature, though I’m not completely sure if that is accurate.

Your game statistics are replaced by the statistics of the creature, though you retain your alignment and your Intelligence, Wisdom, and Charisma scores. You retain the benefit of your own class features. If the target has any class levels, you can't use any of its class features.

Does what it says, nothing more and nothing less. Since it says your stats are replaced and doesn't call out prof. bonus as an exception, you use the prof. bonus of the creature.