Everyone goes after Ron, but I wonder after all the jealous bitchy behaviour she had when he was outperforming her in potions with HBP book and smug behaviour after she says she was right about the book all along makes me think of their friendship would have been as good if Canon Harry was way smarter and outperformed her in school? Hell Ron may have his insecurities on Harry but could Hermione handle being outperformed by Harry?

 

She was fully supportive when he was outperforming her in DADA, she'd still be a good friend if he was better in general. Only problem would be if she didn't approve of methods he used to outperform her, but just being smarter isn't one she'd dislike.

Not like Hermione ever showed hostily towards people like Dumbledore for being vastly better than her.

 

If anything, Hermione was overly trusting of teachers and things like books she saw as authorities on a subject. If Harry fell into that category I don’t see why he’s be different. She’s not resistant to following his lead in the DA.

Her attitude with the HBP potions stuff seemed to originate from the fact that Harry(who was not known for being good at potions) was inexplicably deviating from the original instructions. Then when he explained later, it turns out he was following unsigned random scribbles written on a used textbook.

We know that it’s fine as readers, but it hardly seems like an unreasonable level of caution to not follow instructions when you don’t know what the results will be.

Hell she was even right. Harry went and tried a random spell when he didn’t understand what it was for and nearly murdered Malfoy by accident.

 

The only potential source of tension I see would be if this smarter Harry intentionally or unintentionally exacerbated Hermione's irrational neuroticism about flunking out of school. She could resent him not so much for his superior skill, bur rather for him not feeling the same level of anxiety she does about grades. But even then, that hardly seems like an insurmountable problem or anything.

 

This comes up in the much reviled HPMOR and in the end, they stay close to each other.