This answer is supplementary to the one @guifa wrote.
I agree that the two forms are equivalent in Spanish 99% of the time, and I agree that your teacher might be training you towards a natural choice. But I can think of a tiny difference between the two forms.
A. Let's say you're co-writing a skit with a friend. You're brainstorming. Your friend outlines a possible scene. This is still a very tentative idea. Exploring the idea, you ask, "[If we had the scene start with you crashing a party for a top level UK official, like you said,] what would you be wearing to show your Greenpeace affiliation?" Here the verb form that would fit best would be, "¿Qué estarías llevando para demostrar...?"
B. Now let's imagine that your sister is overhauling her wardrobe with your help. There's some discussion about maybe getting rid of some formal wear taking up space in the closet. You say, "If Aunt Olivia set her wedding date for August, what would you wear?" This would be, "Si Tía Olivia se casara en agosto, ¿qué llevarías?"