While you seem to make a fair point about Stuart Little's abilities, it seems noteworthy that, canon to the book, Stuart's parents were both human, so really he had an unfair advantage over Remy. However, Stuart would not beat Remy in a fight.

First: With the skills Remy has, he could sniff out Stuart before Stuart even got there. He can smell literally every ingredient in food, can smell where his human friend is, and also has the ability to control humans by adopting them as puppets. All he has to do to win is scurry up someone's arm and pull their hair a little, and Stuart wouldn't stand a chance. This brings us to my second point.

Second: With the skill of cooking comes the skill of knife-wielding. Yes, knife-wielding rats would seem like a far-fetched thing, but these are fictional characters we're talking about, so that doesn't really matter, does it? We see in the film that Remy would pick up a cheese knife to defend himself. He would have no problem using that knife on a smaller animal than him because he is, after all, still a rat no matter how you want to look at it.

Third: Stuart has no interest in hurting people. We see in the book AND the film, he does everything possible to avoid harming anyone. This also plays in to how he would no, in fact, win the fight. Also, Remy is BIGGER than Stuart, because Remy is a rat, so even without weapons, in a fur-on-fur battle, Remy would be victorious.

In summation: Remy has the ability to control at least one human, Remy is the only one of them actually proved to be able to wield a knife, and Stuart would have no interest in fighting back. Remy would most certainly win in a fight when pitted against Stuart Little. Besides, what does the ability to sail a boat have to do with fighting? Sailing a toy boat would not be a useful skill in a battle with Stuart's larger, stronger, more skilled cousin.