Costume or uniform? It depends on who's wearing it.
If you're on a team, and everyone wears similar outfits, they're uniforms. The X-Men typically wear uniforms. If it's a non-matching outfit compared to the rest of the team, it's a costume, particularly if it's glittery, spangly, or neon. Kitty got rid of her old costume.
Captain America wears a uniform. When Steve Rogers temporarily used the codename Nomad instead, he made his own costume.
Spider-Man's outfit is almost always a costume. It's awesome, but looks like a circus-performer acrobat's outfit. Except for the Iron-Man-colored one with the extra legs; that one's a uniform.
Superman... can call what he wears a costume or a uniform; it's up to him. Except if he wears the ruffly getup, then it gets called a fashion faux pas.
The Batclan's outfits are always uniforms. Always. (Except for maybe Nightwing's outfit with man-cleavage. See Steve's Nomad costume for why. But he's a former circus performer, so I guess it's forgivable - that and he's hot. ;P)
Wonder Woman's outfit should be armor. I have seen the armor, and it is awesome. What it often ends up as deserves no more title than a star-spangled swimsuit with a quarter of a breastplate added on as an afterthought.
Starting to get the idea? And Scott's just silly. You adorable dorkwad, your outfit is only a costume and not a uniform because it looks like a body-condom! Poor Kitty.