In Lamentations Of The Flame Princess characters start with adventuring clothing. Good clothing to get along. But what makes characters different from each other is style of the clothing. Naturally you write "clothes" on your character sheet but I think that character's style is also important. What colors they prefer and what kind of decoration they like. Even though there usually is only type of clothing written in equipment list player should write what kind of clothing it is. In my opinion describing the style of characters is as important as describing his facial features, body type, eye and hair color etc. Clothing is just extra for how you look like and most certainly personalizes your character further.
In addition to describe your character's looks don't forget to describe his style.