If you do want to analyse discourse, than that should be different from what you mentioned as "text types". Becasue types of text refer to poetry, prose, drama. Discourse is a much more challenging task - it is what the reader/listener sees/hears beyond what is written/heard.

In my opinion, a contrastive approach here would not do. For the simple reason that the theory of discourse is more or less similar in all languages. As a teacher, I would want my students to take a text and "dig into" it, explaining how they understand the mechanism certain structures work by, their function, efect on the reader and text.

An even more challenging activity would be to analyse oral discourse, as that of politicians, for instance.

Well, I hope I was of some help to you.

Good luck!