My brother's a huge Chameleons fan (and I like them too), so I end up listening to a lot of their music whenever he's around. I don't think that The Smiths and The Chameleons have much in common- musically, The Chameleons remind me more of a dark, brooding, early U2. And The Chameleons' vocalist is pretty good, but the lyrics don't hold up to Moz's from what I've heard.
They're certainly worth checking out if you haven't heard them, though- give a listen to Monkeyland, Don't Fall, Swamp Thing, and Caution (for starters).