I really like Slrgear.com for help in choosing a lens/lenses. According to their tests the 105 is all around sharper than the 55. The 105 suffers a bit more from vignetting than the 55, and also a slight increase in CA.
I also have the 18-55 kit lens and had thought about getting the 105 but the cost is too high and considering the market (
eBay, and Craigslist) is flooded with 18-55 that aren't even being sold for 100$ I can't justify the 300$ for a slight increase (almost unnoticeable) in sharpness. Though I would like a wide angle zoom to fill the 55-70mm hole that I have I between lenses. If, and more likely when, I choose to get the wide angle zoom lens my first 3 choices are:
1) Nikon 24-70mm f/2.8 this one is 1800$
2) sigma 24-70mm f/2.8 this one is 900$
3) Nikon 24-120mm f/2.8. This one is 1300$
If your on more of a budget the 16-85 is probably the way to go.
I prefer constant aperture zooms. I also prefer full frame lenses on my D5100 because according to an article I read if the full frame lens suffers from vignetting on a full frame body the effect will be lessened on an DX body because the extreme corners of the glass aren't used. ( if I'm mistaken I hope I will be corrected).
If I were you I would save the money.