One way Nick reports he is different is this:
I believe that on the first night I went to Gatsby's house I was one of the few guests who had actually been invited.
Likewise, Nick had manners. Many of these people came and treated his home and things like an "amusement park". Gatsby had sent one of his chauffeur's over to escort Nick to the house, so Nick really received Gatsby's personal welcome. Most other people just rode on the coattails of someone else.
In The Great Gatsby, at Gatsby's party in chapter three, Nick is an outsider. He is from the Midwest not from the East, and he is not from the same social circles or economic class as the other guests.
He is an outsider throughout the novel. He watches Gatsby's story develop from the outside, without direct involvement. He is present, and performs little tasks like inviting Daisy to tea so Gatsby can be there and meet her after not seeing her for five years, but he is still an outsider.
This is his role as narrator. If he were "one of them," his narration of necessity would be different. But he is not. Not at the party and not at anytime in the novel.
This sets up the contrast between Midwestern values and Eastern, the contrast between the myth of the American Dream and the reality, and the value judgments about easterners like Tom.
If you are looking for a pretty straightforward answer, then I think the answer is probably that he is one of the very few people who has actually been invited to the party. Nick tells us this around the middle of the third page of the chapter. It is page 45 in my edition of the book, with the chapter starting on page 43.
Nick says that many of the other people just come out to Long Island. They are introduced into the party by someone who knows Gatsby. Many of them never even meet Gatsby at the party.
If you're looking for somethign more character-based, I'd say Nick is a more mature person than the other people who are at the party. They just want to get drunk and party. Nick is much more of an adult who seems to actually want to meet and talk to people.