Given that big mom was seemingly dominating every time we saw scenes of the fight, and Kid and Law still haven't used their full strength(Kid hasn't used punk rotten and Law hasn't used his mountain sized room), the tide will probably turn in the next chapter or so.
Kid and Law will go all out and Big Mom will probably take serious damage. Then Big Mom will use awakening and/or ACoC, and get the upper hand again. Then somehow, Kid and/or Law will get a heal and defeat big mom.