Monitors with lots of ghosting and / or input lag feel more sluggish than monitors with less of the mentioned. For example, the dell 2048wfp you had is much worse than the u2412m with these. That would apply for the 2407WFP as well, though I don't know what kind of input lag it has. Compared to these two, your u2412ms should feel faster / snappier in a sense.
The u2412m has very low input lag and is fast for an IPS ghosting wise (though ghosting wise that makes it just average in the LCD world). It should feel decently fast, but it's still not close to a good 120hz display.