I must begin by pointing out that I've never finished the original games for a few reasons, some or all of which might be hidden within my discussion of this topic but I've been given a pretty insightful idea in the previous comments of May's role after the Lilycove battle (The farthest I've made it is to victory road in Sapphire).
Also keep in mind that I've currently just arrived at route 111 after earning the Heat Badge in Alpha Sapphire.
Note: Since I've always played as Brendon after my first two or three gen 3 playthroughs and ergo don't recall him as the rival, I'm just going to exclusively examine May leaving it as a given that most every point I make also applies to Brendon for those who play as May.
Unfortunately, for the most part, the lack of character development that made May the poorest rival of the franchise in the original games still remains, such as how barely established her badge collecting is. Though it's actually one maybe two more than in the originals she mentions gyms so few times that each time she does and most of her appearances, in general, feel very random and inconsistent.
So far one of the most random moments that I've noticed in AS was when she transports you back to Petalsburg claiming she wanted to challenge Norman but then upon arrival wishes YOU luck challenging him and takes off like she totally forgot about doing it herself. O_o
The mentor persona is the biggest flaw; you can't claim that a character yours is meant to always best is the more experienced, that doesn't make a lick of sense especially paired with the earlier discussed (though little supported) fact that she is battling gyms. Some information is missing however that prevents this picture from being completed. Due there being absolutely no backstory of May's character we don't know how much more experience than your character she was supposed to have had and what kind.
One thing that can be determined from your battles with her is that she's not too focused on Pokemon training. Her team is always pretty under grown for the point you're at, so much so that at least in the originals she never fully evolved her starter and then she quits as a trainer after the Lilycove battle with pretty much no rhyme or reason. WTF?!
When you contrast to Barry who was a similar type of rival in D/P/Pt but was strongly driven and frequently showed up to remind you that he was a step ahead of you, hell even to Gary or Silver of R/B/Y/S/G/C May is spotlighted as being horribly written which makes the fact that she was the first friendly rival completely unnoticeable. It's in fact quite difficult to even call her a rival at all and to be honest while I like Barry and even Charen and Bianca of Black and White I kind of feel like it's the a$$hole rivals who were the most exciting.
The two more minor things that have still bothered me about this version of her so far are the fact that she'd correct herself when about to address Birch as 'dad' to your character even though you're kids and not speaking in a professional situation (recall Gary never had reservations about addressing Oak as 'gramps') and as mentioned the facial expressions. I like them but will agree that her tendency to be frozen in the same one for inappropriately long is a bit unsettling even for an anime character.
On a positive note, while little to none of her developmental flaws were touched in Alpha Sapphire and Omega Ruby, I HAVE found some noticeable improvement so far in my play through. The additional interactions with May and her slightly more involved role such as how now she is present and participates in the Meteor Falls scene does establish a stronger relationship with your character. You even get a bit more of a sense that researching Pokemon for Birch (her father) is her true passion.
The way the story was revamped in itself has increased my interest. As a writer myself, one of the things that bugged me about the originals was some of the amateur writing style, as though aimed at Kindergarteners such when you first walk into May's house and the mother begins every single sentence with 'Our daughter'.
"Our daughter was excited to make a new friend. Our daughter is up in her room."
It's so much more mature now and has a much better flow.
So overall, yeah I can tolerate May quite a bit more now but she is still my least favorite rival.