The new version of the 24-120mm Nikkor zoom is certainly better than the previous one. Its constant aperture as well as its interesting focal length makes it a very convenient “everyday lens,” suitable for travel and landscape and even for sports photography (the last was not recommended for the old version).
This said, the behavior of the lens is slightly different depending on the sensor it is coupled with. It will certainly be easier to use on a APS-C body where most of the problems are handled well, especially with respect to vignetting. But an inferior definition on APS-C sensors makes it a less felicitous choice for demanding uses such as sports, for instance.
On a full-frame body, the 24-120mm f/4 can also perform very well. But the photographer will have to stay within an optimal zone, stopping down the lens at f/5.6-8 (depending on the focal length) especially at the shortest focal length, to avoid too much vignetting and too many chromatic aberrations.
Given its price and specs, this lens belongs to the high-end category. As such, one would expect better performance, especially when mounted on full-frame sensors. Indeed, it is a shame that one has to use this lens at 5.6 to keep chromatic aberrations and vignetting low.