Both are the polite way to say. But usually, "입니다" is a literary style from books or used only when you're giving a presentation officially, whereas "이에요" is used as an oral style. In addition, I'd like to correct the nisuxa's answer, when you're talking to someone who is the same age as you, you don't use "이에요" but "(이)야."

입니다 is the "formal style" version of to be. It's primarily used when talking to a stranger, conducting business or official affairs 이에요/에요 is the "polite style" of "ida". It's hard for me to say when to use this style because I rarely use it myself. But, from what I know, use it when you're talking to someone who is the same age as you

"~이에요" is used in any situation as a polite way of expressing, whereas "~입니다." in used in some situations as a polite and formal way of expressing.