Hello, I have a full completion of Baba is you, but I don't know Maxwell as much. Baba basically doens't lead with anything and his first move is dependent on what text is available to him. Assuming everything exists as text, he'll also be able to see Maxwell's properties and potentially break them to nullify them.
Does Maxwell have a leading move or is it the same "puzzle player character" predicament where his first move can be anything? If he does have a leading move, could it even unintentionally break the baba has baba text or bypass it even if the text is isn't anywhere nearby?
Otherwise. Can Maxwell come back from say... Being put to sleep? Simply waking up won't be enough, as baba's rules are persistant as long as they're formed, so he'll immediately fall back asleep unless he can grant himself a resistance to it, but assuming everything exists as text, baba can then null the resistance. (You can then replace "sleep" and ask the same question but with transmutation into a rock, transmutation into baba, erasure, possession and more.)
Baba can target more than just Maxwell though, so if Maxwell makes anything, Baba may have the opportunity to destroy the creation and Maxwell at the same time if he has access to either a combination of NOT and BABA, or ALL. ALL can target Baba himself, but he has ways to survive his own hax or exclude himself from it. This can be extended to Maxwell's equipment as well... In this case, since BABA HAS BABA is in affect, his plan might be to make ALL IS HOT AND MELT to destroy absolutely everything in range while he himself can survive that.
So can Maxwell either disrupt Baba before he forms any more text or breaks text associated with Maxwell, or survive Baba's persistant hax at least once in most scenarios? If neither of those things, I vote baba.