I have the swing that you hang from the ceiling and I love it.
This, I installed a threaded socket directly into the ceiling joist (easy to conceal) so that the eye-bolt can installed and removed.
Even with the ceiling and anchored directly into the joist, I spent some time hanging out (pardon the pun) making sure that it was stable. I would worry that an over the door, would bend the hinges or knock the latch out of alignment and if it were a hollow-core door, I would seriously be worried about damaging the door as well.
I have a studio apartment where they don't allow us to drill into the walls or anything, so a real swing is out of the question. The door I will be using it on is one of the only two doors in my apartment; the front door. It's pretty big and heavy with a deadbolt, so I'm not too worried about the door. I doubt it would work on my bathroom door.
This swing/sling looks to have a seat to sit on. The other ones I looked at are just straps. I am not very strong, so I don't know if I could hold myself up.