By "significantly better" I mean this: you can give a master guitarist a $100 guitar and a $5K guitar and while he/she can produce the same notes on each, the more expensive instrument will sound infinitely better. I would assume it would be the same with a kit lens versus a professional lens. So my question is, is the 18-140 significantly better enough to warrant the cost?
This analogy it is not correct. These two lenses are different. It's like comparing a Strat to a Tele. They both have a distinct sound. It does not make one better then the other, just different.
I have found that when shooting objects in close (ie..flowers or things of this nature) the 28-105 is sharper. However the bokeh on the 18-140 is much nicer and more pleasing.
Shooting landscapes, the 18-140 won hands down on my D7100.
The 28-105 is also a Macro lens. Although it only has 1:2 magnification it makes a very nice macro lens in a pinch. Very sharp.
Once again. Overall, if I was shooting a DX camera and needed a walkaround lens, I would pickup an 18-140.