When attempting a High Jump or Long Jump during a
Sudden Leap, determine the DC using the Long Jump DCs, and
increase your maximum distance to double your Speed.
So i get with a long jump you can set the DC to allow yourself to jump up to double your speed.
For high jump you use the long jump DCs. So a normal high jump is 3 ft vertically and 5 ft horizontally. Is the DC 8 making it easy for the crit success to jump 8ft vertically? Does this allow a higher jump then High jump would normally allow?
I believe that is in fact the case, otherwise the "using the Long Jump DCs" clause would include High Jump's DC as well.
So to summarize, if you wanted you could attempt to high jump double your speed using Sudden Leap, however the DC would be fairly high. It's not unreasonable to expect to be able to jump around 22 feet at level 8 though, discounting any other bonuses to the skill.
That actually makes Sudden Leap very attractive, especially if the barbarian is in a party with limited Ranged damage.
Flying Creatures getting you down? Sudden Leap baby.