differences - "identical with" vs. "identical to"

I find myself always wondering which is the grammatically correct expression or, provided that both are correct, whether there are differences between their meaning. One example:

Passage A in this book is identical to/with passage B in that book.

To me it seems as if both could be used here.

Nonetheless, someone on the net claims that his university's style sheet says that "identical to" is grammatically incorrect and ought to be avoided. (I mention this just as an example)

Yet, the online version of the Oxford Advanced Learner's Dictionary allows both and even makes a difference between their meaning:

Her dress is almost identical to mine.

and

The number on the card should be identical with the one on the chequebook.