Really you should never have a toss up between a many-to-many join and an array in your schema. The right place to use an array would be a case where you were dealing with a one-to-many join with a trivial entity that probably shouldn't be an entity.

That said, arrays are also terribly useful in computation. There are lots of vector operations that really don't make sense on a result set, but that PostgreSQL can compute very efficiently if presented with an array.