To my mind they both fit in and are equivalent but I find both very slightly odd and I don't quite know why. I think "academic status " or "qualifications" would sound better to my ears.
But it is not critical
I think the context of the sentence makes them seem pretty similar in meaning but generally speaking, they do not mean the same thing to me.
'Academic ranking', as Nunty said, is in relation to others. So if she ranks fourth, she must do so in relation to others. There will be three persons before her on the list who have higher grades.
Good 'academic standing' just means that she has met whatever requirements have been set by the institution, including such things as passing classes, paying fees and not breaking the rules.
I agree with gordon that "status" or "qualifications" would work better but if you MUST use one of those words, I suggest, "It looks like her academic ranking had been high enough" instead of "sufficient".