they are the same thing, use the short version to show you are lazy or busy.the longer version is the most commonly used. that said, you won't get any funny looks by saying the short one.

actually, you can use both of them, the staff can understand properly. If you add a measure word such like 一碗、一份，it would be better

你好！一碗蛋汤。 nei hao, yi wan dan tang.

We usually say 蛋花汤or鸡蛋汤。