Things like that always depend on who writes the plot.
Anyone can write a story where either of the monsters wins, but if you have to write it for a audience you have to consider some things.
Popularity: If both monsters are popular you will probably write a story where none of them truly wins or loses.
Otherwise popular monster wins by default, like when traditional Godzilla beat Gino (digital Godzilla) in a matter of seconds in Final Wars.
Good and Evil: If the evil monster is popular, see above. Otherwise you would have the good monster win the fight.
Godzilla has been on both sides, but Cloverfield is definately a enemy of earth. Should Cloverfield attack Godzilla would certainly assume his defender role.
Third party involvement: There may be a unknown force that starts the fight between the monsters for some reason, which would end with both monsters teaming up to beat them in the end.
I would say that Cloverfield is popular enough to warrant a semi draw, but Godzilla would certainly come out on top.
“It appeared that there had even been demonstrations to thank Big Brother for raising the chocolate ration to twenty grams a week. And only yesterday, he reflected, it had been announced that the ration was to be reduced to twenty grams a week. Was it possible that they could swallow that, after only twenty-four hours? Yes, they swallowed it.”
- George Orwell, ‘1984’
