The state transformer approach seems to have advantageous in that it provides a framework for building new monads from old, and accessing the components. One disadvantage is that it lacks symmetry in that one monad is arbitrarily chosen to sit inside the other.
You may want to read "composing monads" by Mark Jones and Luc Duponcheel. It specifies precisely what kind of laws should hold before monads can be composed. (and indeed, it also shows that not all monads are symetrical and can be arbitrarily composed!)
<http://www.cse.ogi.edu/~mpj/pubs/composing.html>
All the best, Daan Leijen.
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