I would say Higher to AH was a much bigger jump than S-Grade to Higher. I enjoyed my AHs (Maths, Applied Maths, Physics & Computing) much more than my Highers in the same subjects. Much more scope to learn about the subject, rather than just what you needed for the exams. And I liked the fact that I could choose pretty much whatever I wanted to do for the physics investigation and the computing course work. Think AHs prepare you much better for University because you have to do quite a bit of the work yourself (i.e. don't have a teacher telling you exactly what to do). Just my 2p...!
Jenn xx