The difference is mostly about routine. If you come in a few days a week, a hot desk is enough. If your desk is your office, take a dedicated one.
A hot desk suits
Freelancers who split their week, teams that work remotely most days, and anyone who does not want to leave things on a desk overnight.
A dedicated desk suits
People who come in every day, need a second screen or their own papers, and want a locker and a fixed place to sit.
A private office suits
Teams of two to twelve who take calls all day, keep client material on the walls or want a door they can close.
Try before you commit
Book a tour and use the free day pass. Most people know within an afternoon.