Speaking of which, what do both characters typically do in battle? What would they likely do in this fight? I'm not really into their respective verses, so call me a secondary.
If Saxi's Luck is active during the fight (Which is about a 50/50 chance), he would likely just stand in the middle of the village and have his luck do the fighting for him.
Saxi's luck functions simularly to Domino's luck from Deadpool 2.
Here is a pretty good example as to how Saxi's luck functions.
If his luck isn't active, he would likely try to use his stealth mastery and range with his boomerang to take out Pinkey from a distance while not getting caught.
Pinkie's toon force also seems to be pretty random. If her toon force ends up helping her out, she will just resort to using her toon force to fight Saxi and try to avoid CQC. If her toon force isn't working or is actively harming her, she will likely try to bring this into a CQC situation.
So in scenario one, we have Saxi's Luck vs Pinkie's Toon Force, with neither really fighting each other. Both of them would likely just stand there as their powers fight the other person. From there, it's just a debate of if Pinkie's toon force is powerful enough to bypass the luck or not.
If neither of their abilities are working, this fight turns into Pinkie trying to find Saxi while Saxi tries to hide and take her out from a distance with his boomerang and pistol. In this fight, Saxi has the edge due to his better experience with weapons, his skill in stealth, and having the AP advantage.
If one of their abilities is working and the other one's abilites aren't, then it's an instant win for the one whose powers are working, as Saxi has no way around the toon force without his luck and Pinkie has no way around the luck without her toon force.
Hope this helps some. I wasn't in the campaign that Pinkie was in, so I am not quite as knowledgeable on her as I am with Saxi.