I wanted to do a theatre EE originally, but I ended up doing an English Lit EE. Why? Because I wanted to explore contextual work (i.e. Waiting for Godot ) and about how its themes were represented in the text. While this sounds like a theatre EE it is technically an English EE because I was exploring the text itself and not the production of Waiting for Godot since different directors may choose something different for the text.
Idk what you want your EE to be specifically about, but if it's about studying the play through the text, it's better off as an english EE.
If you want to write an EE about theatre in specific (e.g. how proxemics influence a character's story arc, or how lighting affects moods of scene or whatever) then a theatre EE would be optimal.
In IB Theatre, a lot of emphasis is placed on the 'creative process' which is fancy way of saying 'how did you come up with this original theatre?'. A very low scoring answer would be 'i saw it online lol' while a higher scoring one would be along the lines of 'I experimented with different ideas of presenting this topic, and I asked a bunch of people what they thought and worked from there." Honestly, IB theatre isnt a great place to start for an EE in theatre unless your EE is specifically about a creative process. If you really need something to work off of, you could read this book by Frantic assembly about their own creative process. Maybe it'll spark your interest which you can then bring to your supervisor. Here's the link --> https://www.amazon.com/Frantic-Assembly-Book-Devising-Theatre/dp/1138777005/ref=dp_ob_title_bk
have fun with your EE!