Conclusion
If I have to pick one of those two lenses, I would definitely go for the Nikon 28-300mm f/3.5-5.6 ED VR. The Nikon 24-120mm f/4G ED VR will probably deliver slightly better results, but as you saw from all the comparisons, the difference in real life pictures is not significant. The longer zoom of the 28-300 lens is much more useful for a "general walk around lens" and the 4mm difference on the wide angle side is almost not noticeable in the pictures.
The 240-120mm focal range overlaps with several other popular lenses in the Nikon's catalog (16-35mm, 24-70mm, 70-200mm) and if you own some of them already, the 28-300mm will make more sense.
If I have to pick one of those two lenses, I would definitely go for the Nikon 28-300mm f/3.5-5.6 ED VR. The Nikon 24-120mm f/4G ED VR will probably deliver slightly better results, but as you saw from all the comparisons, the difference in real life pictures is not significant. The longer zoom of the 28-300 lens is much more useful for a "general walk around lens" and the 4mm difference on the wide angle side is almost not noticeable in the pictures.
The 240-120mm focal range overlaps with several other popular lenses in the Nikon's catalog (16-35mm, 24-70mm, 70-200mm) and if you own some of them already, the 28-300mm will make more sense.