Dawn wins this, hands down. Dawn's journey was handled so much better than May's, as she made mistakes and learned from them. I never got that sense from May; she never really grew as a character.
This is not exactly true. May had the most drastic character development in terms of character in the series, going from someone who was initially disinterested in Pokemon, to then going through constant development with her rivals Drew/Harley, and then learning about the differences between battling like Ash to battling like a coordinator. While I agree with you that Dawn's development was done better in terms of her losing and then learning from them, saying that May never grew is just plain wrong. The May in the very beginning of Hoenn is not the same May as the one from mid/late Hoenn, or the one in Battle Frontier. Her entire personality and attitude toward things completely changed. Her dependence on Ash lessened and her interactions with Drew and Harley changed substantially.
Dawn got the advantage in that we got to see more of her, and contests were developed far more in Sinnoh than they were in Hoenn; they were just as important as Gym Battles, if not more so, since they took up multiple episodes. May was never really more than a side character with a side character's amount of screen-time and character development.
This is wrong. The Contests were treated as just as important as Gyms back in AG too, and I find your statement baffling since most Contests in AG were 2-parters, not to mention there was far more of them. The writers made 15 Contests and two Grand Festivals back in AG, whereas in DP there were only 11 Contests and 1 Grand Festival. Obviously this was because AG was split into two arcs, but considering AG/DP were both 190 episodes long, they still made more of them in AG. Also a lot of DP Contest episodes were only 1 part long (like the two where Dawn loses the appeal round, the one where James wins disguised as Jessie, the one where Kenny beat Ambipom, etc), whereas a lot of May's Contests were 2-parters until BF.
Also you keep saying "side-character" a lot, we know Dawn was a co-star, but saying May didn't get a tremendous amount of screentime compared to the entire rest of the cast is just plain wrong. What would you call Misty/Brock/Iris/Cilan and even Serena then if you call May a side character? None of them got as much attention as May did.
If she needed to train and learn a new strategy, she did it off-screen. Hell, her contests were sometimes off-screen as Ash went off to train and the show focused on him!
This is wrong. Even when Ash went off to train his Pokemon (like Swellow or Snorunt), during a Contest, they never had May's Contests off-screen. We saw all her appeals and most of her battles. The writers also usually skip some battle rounds in Contests and show them as a brief montage to save time, they do this in DP too. In fact, the fact that the writers kept Ash out of all of May's Contests until the very final one, whereas in DP they had Ash compete in Dawn's first Contest and the Wallace Cup, shows that the writers were already willing to take screentime out of Dawn to focus on Ash in a quest he didn't belong in.
I do agree with you that seeing Dawn practice Contest appeals on-screen was really good though, they should have done more of this in AG.
Dawn, by comparison, practically upstaged Ash and took control of the anime for herself, more than once. I was really impressed by the amount of thought and attention given to her, and found myself empathising with her so much more. When May lost I didn't really care; she was beaten by a random character of the day in much the same fashion as Ash. Dawn lost to her biggest rival; it was a fantastic climax to her journey and, whilst I was irritated that she lost, I could see the sense to it. She was never better than Zoey, regardless of how far she'd come throughout the series...and that was fine, because the one who beat her wasn't a faceless extra added for the sole purpose of beating her.
Dawn losing to Zoey kind of puts a damper on her whole journey though. I can understand why the writers did it, but to spend 4 years thinking Dawn was going to improve and get better than Zoey and then it never happened makes rewatching the whole Dawn/Zoey rivalry a bit meh. Zoey was just Dawn's mentor and that's all she was, it also sort of made Zoey into an almost Mary Sue by the end of the saga.
That's actually what I disliked about Dawn's rivalries the most. She had the unbeatable rival (Zoey), and then the two rivals she almost always beat (Kenny and Ursula), and then the one guy she never even battled in a Contest (Nando). There wasn't any real balance between Dawn and her rivals and its odd that we never saw her face Nando in a Contest.
I would hope that if the two battled now, Dawn would win again, but unlike the last time she'd actually deserve to. She did more with herself in one season than May did in two and, unlike May, she has her own distinct style, earned and perfected. Don't get me wrong; I don't dislike May as a character. But compared to Dawn, she might as well be a character of the day for all the development she had.
If they battled again now, you also have to realize May would also be a lot better than the last time we saw her too, so it could go either way. Then again it doesn't really matter.