Stay-Puft, mainly because I don't think Mongo can really do anything offensively against him. Stay-Puft is essentially a walking marshmallow, and would probably absorb anything Mongo did to him. Mongo is more brittle, and I think that would be where he loses, as Stay-Puft's strength would allow him to pull Mongo apart.
However the real winners would be the bystanders. Gingerbread and marshmallow treats for EVERYONE!!!