I like Styx alot. One of those guilty pleasures of mine...
Mine too. I was a big fan of them in my teens and I still like them, especially their first eight albums.
The Serpent Is Rising, Equinox, Grand Illusion - all thoroughly enjoyable as far as I'm concerned.
Having said that, I don't hear anything reminiscent of Styx on ATTW3 or any other album by Genesis.