I would say that the 660 Ti could be a significant upgrade over a 560Ti. The composite price vs performance index from this site's review of the 660 Ti
sort of indicates a minimum average of about 25% increased performance. And here's a review from AnandTech
indicating about 35% increased performance with Battlefield 3 at 1920x1200 - close to the resolution of your new monitor.
The thing is, the new monitor, at 1920x1080, won't demand that much more pixel pushing power than your old 1650x1080 model as your only dealing with about a 16% more pixels. I would think that a 560 Ti should still perform very well at 1080p in pretty much all current games. If the 560 Ti was buttery smooth with your old monitor (which it should be), then it should perform almost as well with the new monitor - or at least close enough as not to make much of a noticeable difference, if any, while gaming. I would definitely try the 560 Ti with the new monitor before upgrading.
If you really like to max out all of the graphics settings in the latest games, the 660 Ti might be a worthwhile upgrade. You definitely don't need
a GTX 670 for 1920x1080 - definitely overkill.
Edit: Forgot the AnandTech link.