Active noise cancelling works by picking up the external noise through microphones in the earpieces and overlaying an inverted signal to block out the sound. In the vast majority of headphones this compromises sound quality in some degree, ranging from an audible hiss to distorting the sound signature, depending on how well it's implemented. There are a few headphones that do a decent job of it, but if sound quality is the top priority and you don't spend your life on public transport or plains, then I would go passive every time.
In terms of recommendations, what music do you listen to? What's your price range?