I think Nietzsche was wary of Wagner's music because he was surprised at how easily seduced/hypnotized he was by it. I can't say I know ANYTHING about Classical music or Wagner (besides what I've read by Nietzsche), but I have read Nietzsche's works multiple times. Vinatge Books publishes a book that begins with Birth of Tragedy (early Nietzsche when he loved Wagner) and ends with The Case of Wagner (late Nietzsche right before his collapse). From what I remember, Nietzsche criticizes Wagner for being overly bombastic and "all over the place," first it's sad, then happy, then sad, then happy, up and down, up and down (schizophrenic/manic-depressive). I think what he's saying is that Wagner was just incredibly manipulative even in his music (not to mention manipulative in their personal relationship). Nietzsche calls Wagner a "genius kitsch," and again I think Nietzsche is saying Wagner just throws a little bit of everything at you but there's no grand, unifying "theme"(?). Wagner's superficial bombast is there to keep you from realizing that underneath it all, he's clueless and offers nothing but quasi-Christianity.
I know this is supposed to be about Strauss, but I just wanted to mention this because I think it's important that Nietzsche didn't criticize Wagner simply because his muisc was "popular."