You have this a bit backwards. Air Assault is a much more physically demanding school than Airborne. There is a 12-mile ruck as the last event. But the school starts with a smoker of an obstacle course, followed by a PT test in ACUs. There will PT in the mornings followed by a 2-mile, 3-mile, 4-mile, and 6-mile ruck march prior to the final 12-miler. That's on top of the slingload inspections and rappelling.
Airborne PT is much easier. They may or may not do a PT test, depending on the cadre and if students all have a valid PT card within 30 days. Long runs, and some time in the pit. Lots of time doing practical events like the swing-landing trainer, the 34-foot mock-exit tower and the big tower (though I have heard they're no longer using them).
You may have the chance to do Pathfinder depending on slotting and successful completion of Air Assault. We had one cadet in our Pathfinder class. He failed out.
If you can, try to get Airborne as a cadet. In the real Army, you won't get jump school unless you go to an airborne billet. You can always get air assault, though, as there are many AASLT satellite schools at different posts.
And they're called Skill Badges. The Girl Scouts wear pins.