I can elaborate on this, based on my own headcanons and theories.
First, let us look at May.
May began a green trainer with no experience whatsoever. She didn't even know handling Pokemon, let alone coordination. However, from there she slowly grew. While most of her development was character development and the skill development was pretty much minimal, she has shown to have one flaw in her battling. Her battle style was influenced by Ash, and so she battles more like him, which means she would use raw power and much more daring techniques. Though May tries to step out of Ash's influence and develop her own style of contest battling through travelling with coordinators like Drew, this trait is something that will remain to some extent. The proof being the way she handled Whirlpool in her matchup against Glaceon. Rather than someone like Zoey, who would try to use Whirpool to showcase her Pokemon, May counters Whirpool with Mirrorcoat's sheer force. Also, her battle with Zoey proves that she's a smart battler. She is pretty good at coming out of a tight spot and make a smart move without prior planning.
Dawn is more performance oriented. She's been wanting to be a coordinator from the beginning. She knew all the basics well (at least better than May did), and knew many stuff about Pokemon coordinating before hand. However, she was disillusioned that contest battling is basically using a couple of flashy moves. She failed miserably thinking so. After enough development, she finally figures this mistake of hers and gets better. Her stronghold is her innovative thinking. The spin technique, the Ice Aqua Jet, the combination moves etc. When compared to May, Dawn concentrates more on showing her Pokemon. She does make some plans on the spot, but it seems like she's actually pretty good at using combination moves she had planned before hand. Unlike May who does things on the spot, Dawn actually relies more on moves prepared well before hand.
So, basically a battle between Dawn and May would boil down to Dawn making a strategy before hand, and May countering it. The winner can be anyone. Unlike battles, contests are a limited time battles. Because of this, "surprise factors" play a major role in contest battling. You surprise your opponent a bit and then take control for 1 minute. Then he will be below you in terms of points. Once you get a significant points lead, you can put constant pressure over your opponent and stop them from performing calmly. If May gets an early point lead, she has higher chances to win. If Dawn gets an early lead, May will have to struggle but still has a chance to win. On the other hand, Dawn can pull a surprise finishing move in the last minute and upset the scoreboard with a quick turnaround.
A battle between Dawn and May would mostly be like this:
May makes frontal attack and gets small point lead.
Dawn settles, and answers with a typical move and equals score.
Dawn uses a powerful combination that brings her the lead and control over May.
May, thanks to her quick thinking will try to turn that lead around. Basically, it will be a struggle for dominance.
The battle is anyone's basically. Both girls have their own plus and minus. Things can turn out either way depending on the way the battle goes, the Pokemon they use etc..