Sure, the characters are equivalent, but a document that has been output is comprised of byte sequences that represent those characters. He didn't realize it, but he's asking about encodings.
Encodings are a weakness in the HTML spec.
Even with HTML 4, there is too much leeway for a document to not signal its own encoding and for a user agent to make wild guesses at what encoding was used. The problem, really, is that he is assuming he can use one encoding for output and can tell his browser to assume a different encoding when it reads the bytes back in. XSLT processors right now only support a limited range of encodings. His browser should be set to auto-detect encodings, if it has that option.