I'm debating which of these two assisted muscle up variations has the most benefit to actually doing a muscle up. I've noticed that while jumping into a muscle up I find myself much lower in the bottom of the dip when compared to the box assisted muscle ups.
The box assisted muscle up forces you to use pulling strength while minimally relying on the legs, teaching the movement to your muscles. The dip is still effective. It seems to be easier to control how tight the rings stay to the body in this version as well.
The jumping muscle up seems to have a stronger benefit in getting through the transitition faster and teaching you to almost dive over the rings and get away from just pulling yourself up as you would in a pull up. The dip is very effective. It seems to be a little harder to control the rings and keeping them tight in this version.
I do question the validity of being able to perform 15 dips and 15 pull ups prior to being able to do a muscle up.