Is PE slower than HF/IB

Not sure how true it is, but from what I’ve read and heard, it seems like PE is almost a border line slow job, not even being able to potentially get carry at big shops for at least 5 years after starting to get carry allocation , which is at least 2-3 years after mba. Meanwhile, even if you don’t make more, it seems like IB (post mba) and HF are more eat what you kill high stress/high energy positions, where you either make a killing, or get shown the door. Is this true?