I think AJ had more a respect for education in general. She doesn't particularly like magic but recognizes its power and potential. Plus, Twilight doesn't really have a job in the community. I think it's Twilight's constant strive to improve herself and help others that AJ respects Twilight for.
As for the Pinkie and Applejack comparison: Applejack is a bit demeaning in her view of others. Not maliciously, but she seems to think that problems she can't grasp aren't problems. Again, narrow lens. She also thinks she knows best. Probably comes from the motherly instincts she's developed raising Applebloom.
Pinkie, on the other hoof, acts with little forethought. She can recognize when someone is suffering but her impulsiveness causes her to make things worse. Filli Vanilli
is the first example to come to mind. She'd rather act immediately to try and help, for better or worse, than take time to consider what would be the best way to help.
While neither are ignorant of others emotions, they struggle to recognize how best to help with those struggles, either through ignorance or ineptitude. @Background Pony #91C5
Yeah, Rainbow screws up a lot. I think she keeps bouncing back to her pride getting in the way because, while it is a frequent source of the problems she faces, she rarely recognizes that her pride is what's leading to her fall. This, after learning a lesson, she views herself as stronger, and better, for it, leading to the loop starting again.