Difference between day a private Equity Consultant and management consultant?

Hello everyone!
New to the consulting world, would love to get some clarity.
I was curious to understand the difference in the day to day work style of a management vs a private equity consultant? Around things like how long does each project last, how much of it is client facing/travel, average working hours (if there is a difference). Is it deck or excel heavy on the CDD side? Or anything in general?  

Also how is a private equity consultant different from a traditional Private equity job? And do the projects work a lot around like a team or an individual consultant?

Thanks!