In general, ribbon tweeters may sometimes have that last nth degree of uber detail or resolution compared to ATM's, but not by much at all. The difference may only make it a little easier to blend ATM's with the mid or woofer compared to ribbon. Ribbons tend to "beam" vertically more than ATM's - another thing that makes for easier driver integration for ATM's.
Ribbons by design have the ribbon itself that is replaceable. It needs to be replaceable because it can get stretched if played too loud, at which point it can lose performance or even break. The cost of a new ribbon is much cheaper than the cost of a new tweeter. ATM's don't have this problem, but they can take SPL's similar to ribbons without damage...but if you go Too far, you'll need to replace the whole tweeter - but, that's mostly only a problem if you're a metalhead or something :>)
I would imagine a Ribbon tweeter produces far more treble detail than any ATM. I usually don't hear any sound from ATMs other than a beeping when the buttons are pressed or the card is ejected.