By far the greatest benefit to requiring student uniforms in American public schools would be the promotion of equality. You're right, students who wear uniforms do interact more than those who don't. Why? Social standing almost always boils down to money. So if everyone wears uniforms, they can't connect based on the fact that they are hundred-dollar Abercrombie & Fitch jeans while others are dressed in Wal-Mart clothing. It erases the lines between lower-middle-class and upper-middle-class, which releases some of the potential social tension. True, even private schools with their uniforms are sectioned into cliques. However, these cliques are based solely on mutual interests, and not who has the most money to blow at the mall.
On the other hand, there is a certain liberation for not having to wear uniforms. More so than anything else, students use their wardrobes at school as a way to express themselves. A person walking past you down the hallway may not say a single word to you, but will probably be judging you on the spot based on your current choice of clothing. It's all about passing judgment.
While I enjoy the ability to dress as I choose, I feel that my high school social life could have been much easier had I attended a private or uniformed school.
The question of which is better comes down to whether or not you support the right to judge people based on their clothing and appearance, because that is the biggest difference between uniformed and casually dressed students.