The battle is new versus old, next gen versus first gen, youth versus experience.
It's quite symbolic. The fact that this match ends in a cliffhanger is one of my favourite things and scenes in Skullgirls story modes.
For a prediction, neither has any reason to hold back. Peacock because she's insane/unaware of the full consequences of her actions/following cartoon logic. Dahlia because she abandoned her conscience years ago, trading her morality for an assassin's career. They're even in that aspect, both would likely go for the kill.
Were I to take a wager though, I'd say: Peacock is more powerful, but Dahlia would win.
A laser gun is fancy and all, but a dagger in the guts never gets outdated.
An inexperienced player will wreak havoc with a S+ char, but a veteran will still defeat him with a low-tier character.
And so on, etc. Peacock barely started the whole fighting thing + doesn't yet have an idea about the full potential of her powers, whereas everything Dahlia could learn about using her toys, she learned + she has years if not decades of killing in her resume.